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Smart DER control for minimizing power losses in distribution feeders
Electric Power Systems Research 109 (2014) 71–79
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Smart DER control for minimizing power losses in distribution feeders Anna Rita Di Fazio ∗ , Giuseppe Fusco, Mario Russo DIEI, Università degli Studi di Cassino e del Lazio Meridionale, 03043 Cassino, Italy
a r t i c l e
i n f o
Article history: Received 8 April 2013 Received in revised form 16 October 2013 Accepted 12 December 2013 Available online 9 January 2014 Keywords: Distributed energy resources Distribution systems Optimization Power losses Reactive power control
a b s t r a c t Distributed energy resources, such as distributed generators and storage systems, are generally considered as active power sources. Indeed, they can also be used as reactive power resources, which contribute to reduce the power losses in a distribution feeder. Adopting a decentralized approach, in this paper an on-line Optimization Strategy is introduced to define the optimal set point of a classical reactive power control system for distributed energy resources so as to minimize the power losses along the feeder. Using only local measurements, firstly the actual operating conditions of the distribution system are estimated and, then, a constraint minimization problem is solved so as to calculate the optimal set point. A suitable change of coordinates yields to evaluate the optimal solution in an analytic closed form. Numerical simulation results are also presented to give evidence of the reduction of power losses and of the performance of the proposed smart control scheme. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In a smart grid, the active and reactive power control systems constitute the control kernel for a large number of distributed energy resources (DERs), including renewable distributed generators (DGs) and storage systems (SSs). There is no question that the primary function of a DER is the transfer of the active power to the distribution grid. The active power generated by a renewable DG is usually controlled to extract the maximum power, according to the availability of the primary energy source (i.e. the maximum power point tracker for photovoltaic generators [1] or the torque pitch control for wind turbines [2]). The active power control of a SS takes into account the state of charge of the battery so as to guarantee an optimal energy exchange with the distribution grid (i.e. for load leveling or balancing and power quality improvement) [3]. The reactive power control systems of DERs regard the opportunity to offer ancillary services to the smart grid. Nowadays, the reactive power injected by DGs is set to a fixed value, required by the distribution system operator to assure an admissible voltage profile in the distribution system with reference to worst-case scenarios of high and low load levels. Usually DGs operate in voltage regulation mode or at constant power factor [4]. The reactive power control of SSs is usually coordinated with the active power charging/discharging of the batteries [3].
∗ Corresponding author. Tel.: +39 07762994366; fax: +39 07762993886. E-mail addresses: [email protected] (A.R. Di Fazio), [email protected] (G. Fusco), [email protected] (M. Russo). 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.12.007
Enhancing the flexibility of DERs is a key factor for the smart grid break-through. Then, it is reasonable that in the foreseeable future the reactive power of DERs will be fully controlled so as to support the reliable, efficient and secure operation of the distribution system. Recently, distribution system operators are becoming more aware of the importance of DER reactive power control and distribution grid codes are changing accordingly, f.i. see the German VDE-AR-N 4105 and the Italian CEI 0-16 and 0-21. However these codes introduce some fixed rules of the DER reactive power variations, which cannot adapt to the changes of the distribution system operating conditions. Research should propose new solutions aiming at the optimal reactive power control in distribution systems with DERs. With reference to the DG optimal control, several methods have been proposed in literature that use centralized or decentralized control structures [5]. When a centralized control structure is used, the reactive powers injected by DG are usually defined by a supervisor unit at the HV/MV substation or at the system control level [6], and large investments for measurements and communication infrastructures are required. On the contrary, when a decentralized control structure is used, the reactive powers are locally determined and communication is required only for coordination purposes [7–9]. According to a completely decentralized approach, in [10,11] a reactive power control scheme for renewable DG has been proposed to improve the voltage profile of a distribution feeder which the DG is connected to. The basic idea is to force the injected DG reactive power to an optimal set point designed on line by solving a simple optimization problem that minimizes the deviation of few feeder voltages from their reference values.
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Fig. 1. Proposed DER reactive power control scheme.
By adopting and extending the decentralized approach just outlined, in this paper a new reactive power control scheme for both DGs and storage systems is proposed so as to minimize the power losses in distribution feeders. An on-line Optimization Strategy (OS) is introduced to define the optimal set point of a classical DER reactive power control scheme. After estimating the Thevenin equivalent circuit of the smart grid, firstly the actual operating conditions of the distribution system are evaluated and then a constraint minimization problem that reduces the power losses in distribution feeders is solved so as to calculate the optimal set point. A suitable change of coordinates yields to evaluate the solution in an analytic closed form. The strong points of the proposed control scheme are to keep the classical structure of a DER control system, to use only local measurements of voltage and current at the Point of Common Coupling (PCC), to limit on-line data exchange with the HV/MV substation to the only case of significant changes of the distribution system structure and to avoid any data exchange with other DERs. The only drawback is related to the modeling approximations that are introduced in presence of multiple DERs and that affect the output of the OS. However, the sub-optimal results obtained by OS are quite close to the optimal ones as shown by numerical simulations. The paper is organized as follows. In Section 2 the DER reactive power control scheme is presented. Then, Section 3 illustrates the proposed OS starting from the modeling assumptions and describing its three steps procedure. Finally, Section 4 reports results of numerical simulations. 2. Reactive power control scheme The classical reactive power control scheme of a DER electronically coupled with the grid is shown in Fig. 1. Starting from the measurements of the voltage vPCC (t) and current iPCC (t) at the PCC node, the injected DER reactive power QPCC (t) is evaluated and compared with the set point Qsp (t) so as to generate a regulation error e(t); the control law u(t) of the reactive power regulator acts on the power electronic converter so as to force the steady-state regulation error to zero. In a centralized approach, the set point Qsp (t) is either assigned on an “a-priori” schedule, based on the forecasted system operating conditions, or received from a supervisor unit at HV/MV substation or system control level. In this paper, adopting a completely decentralized approach, the Qsp (t) is locally determined so as to satisfy an optimization procedure. In this view, the classical reactive power control scheme is enriched with an OS task, as shown in Fig. 1. Using
Fig. 2. Single-line representation of the MV distribution system.
only the local measurements vPCC (t) and iPCC (t), the operating conditions of the smart grid are firstly evaluated and, then, used to calculate the value of Qsp (t) = Qopt that optimizes the power losses in the distribution feeder.
3. Optimization Strategy To develop the smart DER control system, a generic MV distribution system is considered, in which a HV/MV substation, equipped with On Load Tap Changer (OLTC), supplies multiple feeders that can include DGs and SSs (Fig. 2). The OLTC regulation keeps the voltage at MV busbar to a reference value. If the OLTC is equipped with the Line Drop Compensation (LDC), then it regulates the voltage of a fixed node along each feeder. In the following, the OS design is firstly developed for only one DER. Then, the case of multiple DERs equipped with the OS is discussed. Let’s consider in Fig. 2 a specific feeder composed of n nodes and let’s assume that the DER equipped with the smart reactive power control system is connected through the PCC at the mth node of the feeder. To obtain a representation of the system as seen from the PCC, the components of the MV distribution system in Fig. 2 are modeled as follows. Concerning the HV/MV substation, it is modeled by the Thevenin equivalent circuit as seen from the transformer MV busbar. The noload voltage generator V sub and the leakage impedance Z sub may vary in amplitude and phase due to the changes of the HV busbar voltage and to the OLTC action. In the following, a simplified model is adopted in which Z sub does not change and all the changes of the operating conditions are modeled by variations of V sub . The generic ith load Li is modeled by an equivalent shunt admittance Y Li , which is one of the load modeling for distribution systems [12]. The most general load modeling would require the combination of different models (constant power, constant current and constant impedance) [13] to account for different behavior of the loads with respect to the supplying voltages. In the following it is assumed that the equivalent shunt admittance is not constant but can vary so as to account for the changes not only of the loads but also of the network operating conditions. In particular the generic ith load Li is expressed as Y Li = kLi Y load
(1)
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where kLi is a load factor which represents the contribution of Y Li to the total equivalent load admittance Y load . All kLi are assumed to be known and constant while the value of Y load changes according to the system operating conditions. If all the loads Li present the same power factor, kLi are real constants. In practice, the actual load factors can be different from the fixed values that are assumed in the OS and the effects of such approximation are analyzed in the case studies in the following section. The DER is represented by a current injection I PCC depending on the active and reactive powers PPCC and QPCC injected into the network at the mth node and on the nodal voltage V m according to
I PCC =
PPCC − jQ PCC
(2)
Vm
where stands for the complex conjugation. Such a model is general and not related to the type of electric devices and/or of renewable energy source. The configuration of the MV distribution network is assumed to be assigned. Each feeder presents the typical radial topology which is assumed to be known. Indeed, topological reconfiguration of the distribution network must be accounted for. If the possible configurations are a-priori known, then the related information can locally be stored by the OS. In alternative, the new configuration should be communicated ex-post to the OS by the distribution system operator or his distribution management system. This occasional event does not imply particular requirements in terms of communication infrastructure. For the considered feeder, the generic ith line li is modeled by a series impedance Z li , which is assumed to be known. The other feeders connected at the supplying MV busbar, are modeled by an admittance Y no which is evaluated by combining series and parallel lines impedances and load admittances of the other feeders. Eventually, the single-phase electric circuit of the MV distribution system as seen from the PCC is shown in Fig. 3. The block diagram of the proposed OS is shown in Fig. 4. It is composed of three blocks, named respectively Thevenin equivalent parameter estimation, distribution system parameter evaluation and power losses minimization, representing three subtasks to be performed. 3.1. Thevenin equivalent parameter estimation It estimates the parameters of the Thevenin equivalent circuit of the distribution system as seen from the PCC node, which are expressed in terms of the no-load voltage V eq and the equivalent impedance Z eq . To this aim Kalman filters and a constrained recursive least-squares (CRLS) algorithm are used. The Kalman filters extract from the measurements of the voltage vPCC (t) and the current iPCC (t) injected by the DER the corresponding phasors at the fundamental frequency. Then, the CRLS uses such phasors to estimate the parameters of the Thevenin equivalent circuit. When the loads and/or the operating conditions of HV/MV substation change, the values of the estimated parameters vary. The algorithm is able to track such variations provided that the input signals are persistently exciting. Details about the algorithm are in [14,15]. 3.2. Distribution system parameter evaluation It evaluates the operating conditions of the distribution system, expressed in terms of the admittance Y load and the voltage source V sub , representing, respectively, the total connected load and the main supply of the distribution network. This is possible because the previously described modeling assumptions allow to separating
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the effects due to the variations of loads from the ones due to the changes of the operating conditions of the HV/MV substation. Concerning the loads, two considerations have to be made. The first one is that Y load is the only unknown load admittance. In fact, referring to Fig. 3, being the impedances Z sub and Z li assigned, standing equation (1) with given load factors kLi , and the unknown loads admittances Y Li reduce to Y load . The second consideration is that the estimated value Z eq can be used to evaluate the value of Y load . In fact, for a given value of Y load , it is easy to evaluate the value of Z eq by combining series and parallel impedances. However, in this context the inverse problem has to be solved and, unfortunately, the relationship between Z eq and Y load is not explicit and requires the numerical solution of a non linear problem. Using look-up tables improves the computational efficiency of the solving algorithm. Such tables can be filled at the design stage by numerically solving the non linear problem for different Z eq , chosen in an admissible range of values. In operation, the estimated value Z eq is used as entry to the look-up table to determine the total load admittance Y load . Concerning the supplying system, the voltage V sub can be easily derived from the estimation of the V eq . In fact, referring again to Fig. 3, once all the passive parameters of the electric circuit are known, including loads, the value of the voltage V sub can be linked to the value of V eq by applying the classical laws of the electric circuit theory (see also (A.3) in Appendix A).
3.3. Power losses minimization Using the estimates of the operating conditions of the distribution system, this block evaluates the optimal set-point Qopt for the DER voltage/reactive power control scheme by minimizing the power losses Plosses in the feeder while satisfying Power Flow (PF) and Voltage Constraints (VCs). Anyway, the proposed approach can be extended to other objective functions J [6,16]. The optimization problem can be formulated as min
J = Plosses
s.t.
PF VCs
The J is expressed as the sum of the power losses in each line composing the feeder J=
n i=1
Rli Rl2 + Xl2 i
(V i − V i−1 )
2
(3)
i
where Rli and Xli are the resistance and the reactance of the ith line li , respectively. If the OLTC of the HV/MV substation is equipped with LDC, the sum in (3) starts from the node j + 1, being the jth node the last node along the feeder included in the LDC. The PF equations are derived from the electric circuit in Fig. 3. In particular, they are expressed as relations between the nodal voltage and the equivalent voltage and current generators, yielding the set V i = f i V sub + g i I PCC
i = 1, . . ., n
(4)
where f i and g i are complex parameters depending on all the impedances Z li and the admittances Y Li in the electric circuit and where I PCC is given by equation (2). The VC equations are simply the maximum VM and minimum m V values that the nodal voltages are allowed to reach V m ≤ Vi ≤ V M
i = 1, . . ., n
(5)
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Fig. 3. Single-phase circuit of the MV distribution system as seen from the PCC.
Fig. 4. Block diagram of the Optimization Strategy.
The PF equations (2) and (4) can be rewritten as function of V PCC , as described in Appendix A
In the cartesian plane (0, VPCC,R , VPCC,I ), constraint (11) represents a circumference, with center C and radius r equal to
V i = i V sub + ˛i V PCC
C=
PPCC − jQ PCC =
2 VPCC
i = 1, . . ., n
(6)
− f m V sub V PCC
2 2 VPCC,R + VPCC,I − b1 VPCC,R − b2 VPCC,I − b3 PPCC = 0
(8)
2 2 + VPCC,I − b4 VPCC,I + b5 VPCC,R − b6 QPCC = 0 VPCC,R
(9)
where VPCC,R and VPCC,I are, respectively, the real and imaginary parts of V PCC and the parameters b1 , . . ., b6 are equal to
Im{f m V sub g m } b2 = , Re{g m }
Im{f m V sub g m } , b5 = Im{g m }
Re{f m V sub g m } b4 = , Im{g m }
gm 2 b3 = Re{g m }
gm 2 b6 = Im{g m }
min
2 2 J = a1 VPCC,R + a1 VPCC,I + a2 VPCC,R + a3 VPCC,I + a4
2 2 + VPCC,I − b1 VPCC,R − b2 VPCC,I − b3 PPCC = 0 s.t. VPCC,R
Vm ≤
,
b21 4
b2 2
+
b22 4
+ b3
as shown in Fig. 5. By introducing a polar plane (0 , , ı), with the origin 0 ≡ C, constraint (11) is substituted by the equation = r. Taking advantage from this property, the constrained minimization problem can be rewritten as a one-dimensional problem in the variable ı. Details are provided in Appendix 3, yielding min ı
J = a cos ı + b sin ı + c
s.t. ım ≤ ı ≤ ıM
(14)
ıopt = arctan
b
(15)
a
if a cos ıopt + b cos ıopt > 0 otherwise is equal to ıopt + .
(10)
(11)
2 2 c1i VPCC,R + c1i VPCC,I + c2i VPCC,R + c3i VPCC,I + c4i ≤ V M (12)
where Eq. (12) is standing for i = 1, . . ., n.
(13)
The solution ıopt of the problem is
Being PPCC an available measurement derived from vPCC and iPCC , Eq. (8) is function of only VPCC,R and VPCC,I . On the other hand, QPCC is the output of the DER reactive control system and it is a dependent variable of the problem. Then, Eq. (9) can be separated from the optimization problem and used to provide QPCC once V PCC is known. Such simple considerations allow to achieve a useful formulation and to guarantee an effective solution of the optimization problem. In fact, as described in Appendix B, the constraint minimization problem can be written in the variables VPCC,R and VPCC,I and formulated as follows VPCC,R ,VPCC,I
2
r=
Eq. (7) can be split in its real and imaginary parts according to
Re{f m V sub g m } b1 = , Re{g m }
1
(7)
gm
b
Fig. 5. Change of coordinate frame.
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Table 1 Data of the 132/20 kV–24 MVA transformer at the HV/MV substation Type of windings
Ratio for a = 1
Ratio for amin
Ratio for amax
xsub [p.u.]
OLTC positions
Yg
130/20
0.90
1.05
0.08
16
To obtain the optimal voltage V opt , the value of ıopt is directly substituted into the following expression V opt = VPCC,R + jV PCC,I =
b
1
2
+ r cos ıopt
+j
b
2
2
+ r sin ıopt
(16)
Then, the optimal set point Qopt is evaluated by substituting V opt into (9) in place of V PCC . Finally, Qopt must be checked with respect to the allowable range of DER reactive power and, then, sent to the classical reactive power control scheme.
Table 2 Data for both the 20 kV feeders. Line name
Rli []
Xli []
l1 l2 l3 l4 l5 l6 l7 l8
0.34215 0.34215 0.34215 0.34215 0.2281 0.2281 0.2281 0.2281
0.4806 0.4806 0.4806 0.4806 0.3204 0.3204 0.3204 0.3204
3.4. Case of multiple DERs
4. Case studies
The OS design has been developed assuming a single DER along a feeder. In the following some considerations are reported about applying the proposed OS design to the general case of the distribution system shown in Fig. 2 with multiple DERs. First of all, let the case of two DERs installed on two different feeders be considered. Since the voltage at the MV busbar is roughly kept constant by the OLTC action, the power losses along each feeder cannot be significantly affected by the reactive power of the DER installed on the other feeder. Then, DERs on different feeders can be equipped with the OS. In the case of OLTC equipped with LDC, the above consideration is still standing provided that the OS of each DER minimizes the losses along its feeder starting from the node j + 1, being the jth node the last node along the feeder included in the LDC, see (3). A further consideration concerns the case of multiple DERs along the same feeder. In the assumption of avoiding any on-line coordination, only one DER for each feeder can be equipped with the proposed OS. The best candidate is the DER with the highest impact of the feeder power losses and it is identified taking into account both its size and location. The presence of other DERs along the same feeder introduces modeling inaccuracies in the OS design. However, it is possible that different DERs are “electrically distant”. It is the case of some actual feeders along which it is possible to identify some areas with the following characteristics: each area represents a group of nodes whose voltages are strictly coupled and different areas are connected one to another by long distance conductors. In this case one DER for each area can be equipped with the OS while still avoiding any on-line coordination. To identify such areas, some methods presented in literature can be used: in [17] “zones of influence” are identified applying -decomposition [18] to a voltage sensitivity matrix, whereas in [19,20] “voltage load areas” are obtained by a method based on the inherent structure theory of the networks [21,22] applied to the nodal admittance matrix. For each area, the DER which is the best candidate to be equipped with the OS is chosen accounting for both its size and location and its OS minimizes the power losses in the area. In conclusion, the proposed approach, on one side, cannot guarantee the overall loss minimization that can be obtained by acting on all the DERs installed along a feeder, but, on the other side, achieves the best solution that can be reached without additional measurement and communication systems. For this reason, the proposed OS is attractive to improve the performance of present-day distribution systems, postponing the large investments required by the future smart grids.
Reference is made to the 20 kV–50 Hz distribution system shown in Fig. 6, which includes distributed generators as DERs. Two feeders are supplied by a 24 MVA HV/MV transformer which is equipped with an OLTC regulating the voltage of the MV busbar at 1.02 p.u.; the characteristics of the transformer are reported in Table 1. For both the feeders the electric characteristics are reported in Tables 2 and 3. The feeder # 1 includes a 2.0 MW wind DG with OS at node 4 and a 1.0 MW PhotoVoltaic (PV) DG without OS at node 7. Concerning the wind DG, its reactive power injection is limited to ±1.71 MVAr; the rated wind speed is 12 m/s. Concerning the 1.0 MW PV DG, it operates at its rated power and with unity power factor. The feeder # 2 includes a 1.4 MW PV DG at busbar 7 and operates at 100%; it is equipped with OS and its reactive power injection is limited to ±0.85 MVAr. The distribution system has been simulated using PSCAD/EMTDC. 4.1. Steady-state performance In this section the results in terms of steady-state accuracy of the proposed OS are analyzed. To this aim, it is assumed that the wind speed is constant at 12 m/s. The results related to three cases are reported. In the case A, the feeder # 1 operates at full loading conditions whereas the feeder # 2 at half loading conditions. In the case B, the feeder # 1 operates at half loading conditions whereas the feeder # 2 at low loading conditions equal to 25% of the peak load. Finally, in the case C, the same total load as the one assumed in case B is considered but its sharing among the nodes is different. This latter case is useful to analyze the effects of the errors of the load factors on the OS performance. In fact, in the OS development, the load factors are assumed to be known. Their values are derived from historical records of measurements and/or from the load rated powers. Indeed, during operation, the load factors are subject to variations. While their Table 3 Peak loads and rated load factors. Load name
PLi [kW]
L1 L2 L3 L4 L5 L6 L7 L8
156.5 156.5 136.25 136.25 684.25 684.25 1229.0 1229.0
QLi [kVAr] 76.5 76.5 66.675 66.675 334.5 334.5 600.925 600,925
kLr
i
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
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Fig. 6. Simulated distribution system with two feeders and three DGs.
Table 4 Rated versus modified load factors, case C. Feeder # 1
Feeder # 2 kLr
Load
Modified kLi
i
L1 L2 L3 L4 L5 L6 L7 L8
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
kLi −0.0297 −0.0445 −0.0148 0.0297 0.0594 0.0297 −0.0075 −0.0223
0.0652 0.0800 0.0457 0.0012 0.0957 0.1254 0.2860 0.3008
structural variations can be taken into account by using different look-up tables, they are always subject to intrinsic uncertainties due to random load changes. To account for these latter uncertainties, in case C the values of the load factors are significantly changed with respect to the rated ones, by increasing and decreasing the loads in both the feeders. The modified values kLi are reported in Table 4. For the sake of comparison, in Table 4 are also reported the rated values kLr and the differences kLi between the rated and the
Load L1 L2 L3 L4 L5 L6 L7 L8
kLr
i
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
Modified kLi
kLi −0.0223 0.0297 −0.0074 0.0297 −0.0297 −0.0371 −0.0223 0.0594
0.0578 0.0058 0.0383 0.0012 0.1848 0.1922 0.3008 0.2191
Table 6 DG reactive powers and total feeder losses, case B. Control type
OS ORPF UPFC
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
1.36 1.14 0.0
0.39 0.50 0.0
5.6 5.4 10.8
[kW]
i
modified values. For each feeder, the performance of the OSs is compared with the one obtained by a classical control scheme in which the setpoints are fixed; in particular a Unity Power Factor Control (UPFC) is considered. Moreover, the OS performance is compared also with an optimization benchmark. To this aim, a classical Optimal Reactive Power Flow (ORPF) algorithm has been run for the two cases, minimizing the losses on both feeders and assuming the same values of the loads and of the active power injections of the DGs as the ones used in the numerical simulations. In Tables 5–7 the values of the reactive powers of the two DGs with OS and of the total losses along the feeders are reported and
compared with the corresponding values obtained by the UPFC and by the off-line benchmark ORPF, referring respectively to the cases A, B and C. In general, the results show that the OS presents a performance which is very close to the benchmark obtained by the off-line ORPF. In the case A, the values of QPCC are the same with both OS and ORFC because each DG saturates its reactive power injection. In the case B, due to the approximations introduced in the modeling when multiple DERs are present, the OS does not reach the exact optimum represented by the ORPF solution; nevertheless the
Table 5 DG reactive powers and total feeder losses, case A.
Table 7 DG reactive powers and total feeder losses, case C.
Control type
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
OS ORPF UPFC
1.71 1.71 0.0
0.85 0.85 0.0
25.5 25.5 43.7
Control type
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
OS ORPF UPFC
0.79 1.08 0.0
0.47 0.49 0.0
6.3 6.0 11.1
[kW]
[kW]
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
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Fig. 7. Total losses along the feeders versus the average variation of the load factors.
difference in terms of active power losses between the OS and the ORPF is quite limited. In the case C, the OS operates using the rated values kLr . Then, an i
error is introduced in the evaluation of the optimal set-point. From the analysis of Tables 5–7 it is apparent that the results obtained by OS are still good when compared with the ORPF benchmark. It is due to the small sensitivity of the optimal set point to the variations of the load factors, as it is evident comparing the results with the ones in case B. In all the considered cases, the reduction of losses achieved by OS compared to the classical UPFC control is significant and it is obtained by simply making smarter the local reactive set-point design. For the sake of completeness, a sensitivity analysis of the OS performance to the errors on the load factors has been performed. To this aim, while the total load has been kept equal to the one of case B, the load sharing among the nodes has been varied yielding different sets of kLi . Each set is characterized by a value k equal to n r 1 |kLi − kLi | 100 r n kL
k =
i=1
i
which is the average value of the relative variations of kLi with respect to the rated values kLr . In Fig. 7 the values of the total power
Fig. 8. Time evolution of the wind DG injected powers (PPCC , QPCC ), and of the voltages (V0 , V4 , V8 ) for feeder #1 in case B with wind speed variations.
The results of a 20 simulation are reported in Fig. 8, showing the time evolution of the injected powers PPCC and QPCC of the wind DG and of the voltage amplitudes V0 , V4 and V8 of feeder # 1 in the case B. The OS is initialized with QPCC at its maximum value (1.71 MVAr). At about t = 1 the OS starts working, corrects the optimal set-point and decreases QPCC . During the subsequent transient, also the OLTC varies its operating conditions (see V0 ). Between t = 1 and t = 3 .5 there is also a steep increase of PPCC due to wind speed variation. Consequently, the OS changes the reactive power injection, increasing its value so as to reduce losses. After t = 3 .5 , PPCC is subject to some slower variations, which are tracked by the OS by varying consequently QPCC . The effects of these active and reactive power injections on the voltage profile along the feeder # 1 are also evident in Fig. 8; as expected, the voltage V0 is quite constant whereas the voltages V4 and V8 are subject to larger variations.
i
losses along the feeders Ploss versus k are reported with reference to the OS and the ORPF. The ORPF uses the actual load factors and can be thus assumed as the benchmark. The OS uses the rated values kLr and consequently evaluates a sub-optimal solution. Anyway, i
analyzing Fig. 7, the robustness of the OS is quite evident even in presence of huge errors on the values of the load factors. In particular, for a value of k equal to about 90% the resulting error on the power losses is equal to 1.5%. 4.2. Dynamic performance In actual applications, the wind DG does not operate with constant wind speed but it is subject to random variations of the energy source, which cause changes of the injected active power. Then, in this subsection it is tested the ability of the OS to track the optimal set-point in presence of such random variations. Numerical simulation have been performed with reference to the case B, as defined in the previous section. The time evolution of the wind speed has been obtained by combining the effects of the variation of its mean value with a noise. The former variation is obtained from actual measurements [23], whereas the noise is obtained by using the wind gust model available from PSCAD library.
5. Conclusion In this paper a new reactive power control scheme for DERs has been proposed so as to minimize the power losses in a smart distribution grid. The classical DER reactive power control scheme has been enriched by an on-line Optimization Strategy, whose strong points are: to keep the classical structure of a DER control system, to use only local measurements of voltage and current at the PCC, to account for the changes of the operating conditions of the distribution system, to limit on-line data exchange with the HV/MV substation to the only case of significant changes of the distribution system structure and to avoid any data exchange with other DERs. The only drawback is related to the modelling approximations that are introduced in presence of multiple DERs and that cause inaccuracies in the output of the Optimization Strategy. Numerical simulation results have evidenced the improvements of the performance by adopting the proposed Optimization Strategy, which proved to give suboptimal results very close to the optimal ones. Acknowledgment The authors acknowledge the financial support to this research by GETRA S.p.A.
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Appendix A.
In a similar way, by substituting into (3) the constraint (6), VCs can be expressed as function of V i as
The nodal voltage V PCC at PCC node can be expressed as function of either the Thevenin equivalent parameters
V m ≤ |V i = i V sub + ˛i V PCC | ≤ V M
V PCC = V eq + Z eq I PCC
(A.1)
V PCC = f m V sub + g m I PCC
(A.2)
Comparing Eqs. (A.1) and (A.2), it derives fm =
V eq
(A.3)
By substituting into (2) and (4) the expression of I PCC derived from (A.1) it is obtained V i = f i V sub + g i
V PCC − V eq
i = 1, . . ., n
Z eq
PPCC − jQPCC = V PCC
(A.4)
gif m gm
V PCC − V eq
where c1i , . . ., c4i for i = 1, . . ., n are equal to
c2i = 2(Re{i V sub }Re{˛i } + Im{i V sub }Im{˛i })
(B.10)
c3i = 2(−Re{i V sub }Im{˛i } + Im{i V sub }Re{˛i })
(B.11)
c4i = (i V sub )
(A.5)
Z eq
V i = i V sub + ˛i V PCC
gi gm
i = 1, . . ., n
(A.6)
i = 1, . . ., n
(A.7)
2 −f V VPCC m sub V PCC
(A.8)
gm
Appendix B. The objective function J can be expressed as function of V i by substituting into (3) the expression of the PF constraint given by (6) J=
Rli Rl2 + Xl2
i=1
i
(i V sub + ˛i V PCC − i−1 V sub − ˛i−1 V PCC )
2
(B.1)
i
Then, being V sub , i and ˛i known once V eq and Z eq are estimated, J can be rewritten as function of VPCC,R and VPCC,I as follows J=
n
2 a1 VPCC,R
2
VPCC,R =
b1 + cos ı 2
(C.1)
VPCC,I =
b2 + sin ı 2
(C.2)
2 + a1 VPCC,I
+ a2 VPCC,R + a3 VPCC,I + a4
By substituting Eqs. (C.1) and (C.2) into (10)–(12), the expression of J, PF and VCs are replaced by J = d1 cos ı + d2 sin ı + d3 2 + d4
(C.3)
=r
(C.4)
Vm ≤
d1i cos ı + d2i sin ı + d3i + d4i ≤ V M
d1 = a1 b1 + a2
(C.6)
d2 = a1 b2 + a3
(C.7)
d3 = a1
(C.8)
d4 = a1
b21 4
(B.2)
where a1 =
i=1
Rli Rl2 + Xl2 i
i=1
2
+
i=1
a4 =
i=1
Re{V sub (˛i − ˛i−1 ) (i − i−1 )} 2
Rl2 + Xl i
Rli
+ a2
b1 b2 + a3 + a4 2 2
Rli Rl2 + Xl2
(C.10)
d2i = c1i b2 + c3i
b2 2
(C.11)
i
2
(C.12) b21 4
+ c1i
b22 4
+ c4
(C.13)
Substituting the constraint (C.4) into (C.3), the J changes into (B.5)
i
2 Vsub (˛i − ˛i−1 )
(C.9)
b1 2
d4i = c1i
i
i
4
d1i = c1i b1 + c2i
(B.4)
i
Im{V sub (˛i − ˛i−1 ) (i − i−1 )} 2
Rl2 + Xl
n
(B.3)
b2
d3i = c1i
Rli
n
a3 = 2
2
i
n
a2 = 2
(˛i − ˛i−1 )
i = 1, . . ., n (C.5)
where
i=1
n
(B.12)
Appendix C.
yields
n
(B.9)
The cartesian coordinates VPCC,R and VPCC,I in the polar plan are expressed as
˛i =
PPCC − jQPCC =
2 2 c1i VPCC,R + c1i VPCC,I + c2i VPCC,R + c3i VPCC,I + c4i ≤ V M (B.8)
for i = 1, . . ., n.
Finally, imposing i = fi −
c1i = ˛2i
g m = Z eq
V sub
(B.7)
and, then, rewritten in terms of VPCC,R and VPCC,I as Vm ≤
or the electric circuit parameters
i = 1, . . ., n
J = a cos ı + b sin ı + c
(C.14)
with a = rd1 , b = rd2 , c = r2 d3 + d4 . In a similar way, the VCs in (C.5) becomes (B.6)
Vm ≤
di cos ı + ei sin ı + fi ≤ V M
i = 1, . . ., n
(C.15)
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
with di = rd1i , ei = rd2i , fi = rd3i + d4i . To rewritten the box constraints (C.15) in terms of ım ≤ ı ≤ ıM
(C.16) Vm
VM
the boundary values and are mapped into the variable ı, by calculating the closed-form analytic solution ılim of the following i equation once for Vlim = Vm and then for Vlim = VM 2 di cos ılim + ei sin ılim + fi = Vlim i i
i = 1, . . ., n
(C.17)
It yields n values ım and ıM for both the minimum and maximum i i values of ı. The boundary values ım and ıM are trivially evaluated } and the min{ıM } respectively. as the max{ım i i References [1] A. Yazdani, A.R. Di Fazio, H. Ghoddami, M. Russo, M. Kazerani, J. Jatskevich, K. Strunz, S. Leva, J. Martinez, Modeling guidelines and a benchmark for power system simulation studies of three-phase single-stage photovoltaic systems, IEEE Trans. Power Deliv. 26 (2) (2011) 1247–1264. [2] J.H. Laks, L.Y. Pao, A.D. Wright, Control of wind turbines: past, present, and future, in: American Control Conference ACC’09, 2009, pp. 2096–2103. [3] M.H. Nehrir, C. Wang, K. Strunz, H. Aki, R. Ramakumar, J. Bing, Z. Miao, Z. Salameh, A review of hybrid renewable/alternative energy systems for electric power generation: configurations, control, and applications, IEEE Trans. Sustain. Energy 2 (4) (2011) 392–403. [4] T.W. Eberly, R.C. Schaefer, Voltage versus var/power-factor regulation on synchronous generators, IEEE Trans. Ind. Appl. 38 (6) (2002) 1682–1687. [5] P. Vovos, A. Kiprakis, A. Wallace, G. Harrison, Centralized and distributed voltage control: impact on distributed generation penetration, IEEE Trans. Power Syst. 22 (1) (2007) 476–483. [6] A. Aquino-Lugo, R. Klump, T. Overbye, A control framework for the smart grid for voltage support using agent-based technologies, IEEE Trans. Smart Grid 2 (1) (2011) 173–180. [7] P. Carvalho, P. Correia, L. Ferreira, Distributed reactive power generation control for voltage rise mitigation in distribution networks, IEEE Trans. Power Syst. 23 (2) (2008) 766–772.
79
[8] K. Tanaka, M. Oshiro, S. Toma, A. Yona, T. Senjyu, T. Funabashi, C.-H. Kim, Decentralised control of voltage in distribution systems by distributed generators, IEE Proc. Generat. Transm. Distrib. 4 (11) (2010) 1251–1260. [9] H.E. Farag, E.F. El-Saadany, R. Seethapathy, A two ways communication-based distributed control for voltage regulation in smart distribution feeders, IEEE Trans. Smart Grid 3 (1) (2012) 271–281. [10] A.R. Di Fazio, G. Fusco, M. Russo, Optimisation strategy applied to DG reactive power for decentralised voltage control in smart grids, in: Cigrè International Symposium, The Electric Power System of the Future, Bologna, Italy, 2011. [11] A.R. Di Fazio, G. Fusco, M. Russo, Decentralised voltage regulation in smart grids using reactive power from renewable DG, in: IEEE International Energy Conference & Exhibition ENERGYCON 2012, Florence, Italy, 2012. [12] I.D.P.W.G. Report, Radial distribution test feeders, IEEE Trans. Power Syst. 6 (3) (1991) 975–985. [13] W.H. Kersting, Distribution System Modeling and Analysis, CRC Press LLC, Boca Raton, Florida, USA, 2002. [14] G. Fusco, A. Losi, M. Russo, Constrained least squares methods for parameter tracking of power system steady-state equivalent circuits, IEEE Trans. Power Deliv. 15 (3) (2000) 1073–1080. [15] G. Fusco, M. Russo, Adaptive Voltage Control in Power Systems – Modeling, Design and Applications, Advances in Industrial Control, Springer, London, UK, 2007. [16] K. Rogers, R. Klump, H. Khurana, A. Aquino-Lugo, T. Overbye, An authenticated control framework for distributed voltage support on the smart grid, IEEE Trans. Smart Grid 1 (1) (2010) 40–47. [17] L. Yu, D. Czarkowski, F. de León, Optimal distributed voltage regulation for secondary networks with DGs, IEEE Trans. Smart Grid 3 (2) (2012) 959–967. ˇ [18] D.D. Siljak, Decentralized Control of Complex Systems, Mathematics in Science and Engineering, vol. 184, Academic Press, San Diego, CA, 1991. [19] G. Valtorta, et al., Prototypes and algorithms for network management, providing the signals sent by the DSOs to the aggregators and the markets, enabling and exploiting active demand, Deliverable D3.1, ADDRESS Consortium EU-FP7, 2011 http://www.addressfp7.org [20] G.M. Casolino, A.R. Di Fazio, A. Losi, M. Russo, Smart modelling and tools for distribution system management and operation, in: IEEE International Energy Conference & Exhibition ENERGYCON 2012, Florence, Italy, 2012. [21] M.A. Laughton, M.A. El-Iskandarani, The structure of power network voltage profiles, in: 7th Power Systems Computation Conference PSCC, Lausanne, Switzerland, 1982, pp. 845–851. [22] G. Carpinelli, A. Russo, M. Russo, P. Verde, Inherent structure theory of networks and power system harmonics, IEE Proceedings on Generation–Transmission & Distribution 145 (2) (1998) 123–132. [23] NREL, MDIC/SRRL base line measurement system (December 2011). http://www.nrel.gov/midc/srrl bms
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Smart DER control for minimizing power losses in distribution feeders Anna Rita Di Fazio ∗ , Giuseppe Fusco, Mario Russo DIEI, Università degli Studi di Cassino e del Lazio Meridionale, 03043 Cassino, Italy
a r t i c l e
i n f o
Article history: Received 8 April 2013 Received in revised form 16 October 2013 Accepted 12 December 2013 Available online 9 January 2014 Keywords: Distributed energy resources Distribution systems Optimization Power losses Reactive power control
a b s t r a c t Distributed energy resources, such as distributed generators and storage systems, are generally considered as active power sources. Indeed, they can also be used as reactive power resources, which contribute to reduce the power losses in a distribution feeder. Adopting a decentralized approach, in this paper an on-line Optimization Strategy is introduced to define the optimal set point of a classical reactive power control system for distributed energy resources so as to minimize the power losses along the feeder. Using only local measurements, firstly the actual operating conditions of the distribution system are estimated and, then, a constraint minimization problem is solved so as to calculate the optimal set point. A suitable change of coordinates yields to evaluate the optimal solution in an analytic closed form. Numerical simulation results are also presented to give evidence of the reduction of power losses and of the performance of the proposed smart control scheme. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In a smart grid, the active and reactive power control systems constitute the control kernel for a large number of distributed energy resources (DERs), including renewable distributed generators (DGs) and storage systems (SSs). There is no question that the primary function of a DER is the transfer of the active power to the distribution grid. The active power generated by a renewable DG is usually controlled to extract the maximum power, according to the availability of the primary energy source (i.e. the maximum power point tracker for photovoltaic generators [1] or the torque pitch control for wind turbines [2]). The active power control of a SS takes into account the state of charge of the battery so as to guarantee an optimal energy exchange with the distribution grid (i.e. for load leveling or balancing and power quality improvement) [3]. The reactive power control systems of DERs regard the opportunity to offer ancillary services to the smart grid. Nowadays, the reactive power injected by DGs is set to a fixed value, required by the distribution system operator to assure an admissible voltage profile in the distribution system with reference to worst-case scenarios of high and low load levels. Usually DGs operate in voltage regulation mode or at constant power factor [4]. The reactive power control of SSs is usually coordinated with the active power charging/discharging of the batteries [3].
∗ Corresponding author. Tel.: +39 07762994366; fax: +39 07762993886. E-mail addresses: [email protected] (A.R. Di Fazio), [email protected] (G. Fusco), [email protected] (M. Russo). 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.12.007
Enhancing the flexibility of DERs is a key factor for the smart grid break-through. Then, it is reasonable that in the foreseeable future the reactive power of DERs will be fully controlled so as to support the reliable, efficient and secure operation of the distribution system. Recently, distribution system operators are becoming more aware of the importance of DER reactive power control and distribution grid codes are changing accordingly, f.i. see the German VDE-AR-N 4105 and the Italian CEI 0-16 and 0-21. However these codes introduce some fixed rules of the DER reactive power variations, which cannot adapt to the changes of the distribution system operating conditions. Research should propose new solutions aiming at the optimal reactive power control in distribution systems with DERs. With reference to the DG optimal control, several methods have been proposed in literature that use centralized or decentralized control structures [5]. When a centralized control structure is used, the reactive powers injected by DG are usually defined by a supervisor unit at the HV/MV substation or at the system control level [6], and large investments for measurements and communication infrastructures are required. On the contrary, when a decentralized control structure is used, the reactive powers are locally determined and communication is required only for coordination purposes [7–9]. According to a completely decentralized approach, in [10,11] a reactive power control scheme for renewable DG has been proposed to improve the voltage profile of a distribution feeder which the DG is connected to. The basic idea is to force the injected DG reactive power to an optimal set point designed on line by solving a simple optimization problem that minimizes the deviation of few feeder voltages from their reference values.
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Fig. 1. Proposed DER reactive power control scheme.
By adopting and extending the decentralized approach just outlined, in this paper a new reactive power control scheme for both DGs and storage systems is proposed so as to minimize the power losses in distribution feeders. An on-line Optimization Strategy (OS) is introduced to define the optimal set point of a classical DER reactive power control scheme. After estimating the Thevenin equivalent circuit of the smart grid, firstly the actual operating conditions of the distribution system are evaluated and then a constraint minimization problem that reduces the power losses in distribution feeders is solved so as to calculate the optimal set point. A suitable change of coordinates yields to evaluate the solution in an analytic closed form. The strong points of the proposed control scheme are to keep the classical structure of a DER control system, to use only local measurements of voltage and current at the Point of Common Coupling (PCC), to limit on-line data exchange with the HV/MV substation to the only case of significant changes of the distribution system structure and to avoid any data exchange with other DERs. The only drawback is related to the modeling approximations that are introduced in presence of multiple DERs and that affect the output of the OS. However, the sub-optimal results obtained by OS are quite close to the optimal ones as shown by numerical simulations. The paper is organized as follows. In Section 2 the DER reactive power control scheme is presented. Then, Section 3 illustrates the proposed OS starting from the modeling assumptions and describing its three steps procedure. Finally, Section 4 reports results of numerical simulations. 2. Reactive power control scheme The classical reactive power control scheme of a DER electronically coupled with the grid is shown in Fig. 1. Starting from the measurements of the voltage vPCC (t) and current iPCC (t) at the PCC node, the injected DER reactive power QPCC (t) is evaluated and compared with the set point Qsp (t) so as to generate a regulation error e(t); the control law u(t) of the reactive power regulator acts on the power electronic converter so as to force the steady-state regulation error to zero. In a centralized approach, the set point Qsp (t) is either assigned on an “a-priori” schedule, based on the forecasted system operating conditions, or received from a supervisor unit at HV/MV substation or system control level. In this paper, adopting a completely decentralized approach, the Qsp (t) is locally determined so as to satisfy an optimization procedure. In this view, the classical reactive power control scheme is enriched with an OS task, as shown in Fig. 1. Using
Fig. 2. Single-line representation of the MV distribution system.
only the local measurements vPCC (t) and iPCC (t), the operating conditions of the smart grid are firstly evaluated and, then, used to calculate the value of Qsp (t) = Qopt that optimizes the power losses in the distribution feeder.
3. Optimization Strategy To develop the smart DER control system, a generic MV distribution system is considered, in which a HV/MV substation, equipped with On Load Tap Changer (OLTC), supplies multiple feeders that can include DGs and SSs (Fig. 2). The OLTC regulation keeps the voltage at MV busbar to a reference value. If the OLTC is equipped with the Line Drop Compensation (LDC), then it regulates the voltage of a fixed node along each feeder. In the following, the OS design is firstly developed for only one DER. Then, the case of multiple DERs equipped with the OS is discussed. Let’s consider in Fig. 2 a specific feeder composed of n nodes and let’s assume that the DER equipped with the smart reactive power control system is connected through the PCC at the mth node of the feeder. To obtain a representation of the system as seen from the PCC, the components of the MV distribution system in Fig. 2 are modeled as follows. Concerning the HV/MV substation, it is modeled by the Thevenin equivalent circuit as seen from the transformer MV busbar. The noload voltage generator V sub and the leakage impedance Z sub may vary in amplitude and phase due to the changes of the HV busbar voltage and to the OLTC action. In the following, a simplified model is adopted in which Z sub does not change and all the changes of the operating conditions are modeled by variations of V sub . The generic ith load Li is modeled by an equivalent shunt admittance Y Li , which is one of the load modeling for distribution systems [12]. The most general load modeling would require the combination of different models (constant power, constant current and constant impedance) [13] to account for different behavior of the loads with respect to the supplying voltages. In the following it is assumed that the equivalent shunt admittance is not constant but can vary so as to account for the changes not only of the loads but also of the network operating conditions. In particular the generic ith load Li is expressed as Y Li = kLi Y load
(1)
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
where kLi is a load factor which represents the contribution of Y Li to the total equivalent load admittance Y load . All kLi are assumed to be known and constant while the value of Y load changes according to the system operating conditions. If all the loads Li present the same power factor, kLi are real constants. In practice, the actual load factors can be different from the fixed values that are assumed in the OS and the effects of such approximation are analyzed in the case studies in the following section. The DER is represented by a current injection I PCC depending on the active and reactive powers PPCC and QPCC injected into the network at the mth node and on the nodal voltage V m according to
I PCC =
PPCC − jQ PCC
(2)
Vm
where stands for the complex conjugation. Such a model is general and not related to the type of electric devices and/or of renewable energy source. The configuration of the MV distribution network is assumed to be assigned. Each feeder presents the typical radial topology which is assumed to be known. Indeed, topological reconfiguration of the distribution network must be accounted for. If the possible configurations are a-priori known, then the related information can locally be stored by the OS. In alternative, the new configuration should be communicated ex-post to the OS by the distribution system operator or his distribution management system. This occasional event does not imply particular requirements in terms of communication infrastructure. For the considered feeder, the generic ith line li is modeled by a series impedance Z li , which is assumed to be known. The other feeders connected at the supplying MV busbar, are modeled by an admittance Y no which is evaluated by combining series and parallel lines impedances and load admittances of the other feeders. Eventually, the single-phase electric circuit of the MV distribution system as seen from the PCC is shown in Fig. 3. The block diagram of the proposed OS is shown in Fig. 4. It is composed of three blocks, named respectively Thevenin equivalent parameter estimation, distribution system parameter evaluation and power losses minimization, representing three subtasks to be performed. 3.1. Thevenin equivalent parameter estimation It estimates the parameters of the Thevenin equivalent circuit of the distribution system as seen from the PCC node, which are expressed in terms of the no-load voltage V eq and the equivalent impedance Z eq . To this aim Kalman filters and a constrained recursive least-squares (CRLS) algorithm are used. The Kalman filters extract from the measurements of the voltage vPCC (t) and the current iPCC (t) injected by the DER the corresponding phasors at the fundamental frequency. Then, the CRLS uses such phasors to estimate the parameters of the Thevenin equivalent circuit. When the loads and/or the operating conditions of HV/MV substation change, the values of the estimated parameters vary. The algorithm is able to track such variations provided that the input signals are persistently exciting. Details about the algorithm are in [14,15]. 3.2. Distribution system parameter evaluation It evaluates the operating conditions of the distribution system, expressed in terms of the admittance Y load and the voltage source V sub , representing, respectively, the total connected load and the main supply of the distribution network. This is possible because the previously described modeling assumptions allow to separating
73
the effects due to the variations of loads from the ones due to the changes of the operating conditions of the HV/MV substation. Concerning the loads, two considerations have to be made. The first one is that Y load is the only unknown load admittance. In fact, referring to Fig. 3, being the impedances Z sub and Z li assigned, standing equation (1) with given load factors kLi , and the unknown loads admittances Y Li reduce to Y load . The second consideration is that the estimated value Z eq can be used to evaluate the value of Y load . In fact, for a given value of Y load , it is easy to evaluate the value of Z eq by combining series and parallel impedances. However, in this context the inverse problem has to be solved and, unfortunately, the relationship between Z eq and Y load is not explicit and requires the numerical solution of a non linear problem. Using look-up tables improves the computational efficiency of the solving algorithm. Such tables can be filled at the design stage by numerically solving the non linear problem for different Z eq , chosen in an admissible range of values. In operation, the estimated value Z eq is used as entry to the look-up table to determine the total load admittance Y load . Concerning the supplying system, the voltage V sub can be easily derived from the estimation of the V eq . In fact, referring again to Fig. 3, once all the passive parameters of the electric circuit are known, including loads, the value of the voltage V sub can be linked to the value of V eq by applying the classical laws of the electric circuit theory (see also (A.3) in Appendix A).
3.3. Power losses minimization Using the estimates of the operating conditions of the distribution system, this block evaluates the optimal set-point Qopt for the DER voltage/reactive power control scheme by minimizing the power losses Plosses in the feeder while satisfying Power Flow (PF) and Voltage Constraints (VCs). Anyway, the proposed approach can be extended to other objective functions J [6,16]. The optimization problem can be formulated as min
J = Plosses
s.t.
PF VCs
The J is expressed as the sum of the power losses in each line composing the feeder J=
n i=1
Rli Rl2 + Xl2 i
(V i − V i−1 )
2
(3)
i
where Rli and Xli are the resistance and the reactance of the ith line li , respectively. If the OLTC of the HV/MV substation is equipped with LDC, the sum in (3) starts from the node j + 1, being the jth node the last node along the feeder included in the LDC. The PF equations are derived from the electric circuit in Fig. 3. In particular, they are expressed as relations between the nodal voltage and the equivalent voltage and current generators, yielding the set V i = f i V sub + g i I PCC
i = 1, . . ., n
(4)
where f i and g i are complex parameters depending on all the impedances Z li and the admittances Y Li in the electric circuit and where I PCC is given by equation (2). The VC equations are simply the maximum VM and minimum m V values that the nodal voltages are allowed to reach V m ≤ Vi ≤ V M
i = 1, . . ., n
(5)
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A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
Fig. 3. Single-phase circuit of the MV distribution system as seen from the PCC.
Fig. 4. Block diagram of the Optimization Strategy.
The PF equations (2) and (4) can be rewritten as function of V PCC , as described in Appendix A
In the cartesian plane (0, VPCC,R , VPCC,I ), constraint (11) represents a circumference, with center C and radius r equal to
V i = i V sub + ˛i V PCC
C=
PPCC − jQ PCC =
2 VPCC
i = 1, . . ., n
(6)
− f m V sub V PCC
2 2 VPCC,R + VPCC,I − b1 VPCC,R − b2 VPCC,I − b3 PPCC = 0
(8)
2 2 + VPCC,I − b4 VPCC,I + b5 VPCC,R − b6 QPCC = 0 VPCC,R
(9)
where VPCC,R and VPCC,I are, respectively, the real and imaginary parts of V PCC and the parameters b1 , . . ., b6 are equal to
Im{f m V sub g m } b2 = , Re{g m }
Im{f m V sub g m } , b5 = Im{g m }
Re{f m V sub g m } b4 = , Im{g m }
gm 2 b3 = Re{g m }
gm 2 b6 = Im{g m }
min
2 2 J = a1 VPCC,R + a1 VPCC,I + a2 VPCC,R + a3 VPCC,I + a4
2 2 + VPCC,I − b1 VPCC,R − b2 VPCC,I − b3 PPCC = 0 s.t. VPCC,R
Vm ≤
,
b21 4
b2 2
+
b22 4
+ b3
as shown in Fig. 5. By introducing a polar plane (0 , , ı), with the origin 0 ≡ C, constraint (11) is substituted by the equation = r. Taking advantage from this property, the constrained minimization problem can be rewritten as a one-dimensional problem in the variable ı. Details are provided in Appendix 3, yielding min ı
J = a cos ı + b sin ı + c
s.t. ım ≤ ı ≤ ıM
(14)
ıopt = arctan
b
(15)
a
if a cos ıopt + b cos ıopt > 0 otherwise is equal to ıopt + .
(10)
(11)
2 2 c1i VPCC,R + c1i VPCC,I + c2i VPCC,R + c3i VPCC,I + c4i ≤ V M (12)
where Eq. (12) is standing for i = 1, . . ., n.
(13)
The solution ıopt of the problem is
Being PPCC an available measurement derived from vPCC and iPCC , Eq. (8) is function of only VPCC,R and VPCC,I . On the other hand, QPCC is the output of the DER reactive control system and it is a dependent variable of the problem. Then, Eq. (9) can be separated from the optimization problem and used to provide QPCC once V PCC is known. Such simple considerations allow to achieve a useful formulation and to guarantee an effective solution of the optimization problem. In fact, as described in Appendix B, the constraint minimization problem can be written in the variables VPCC,R and VPCC,I and formulated as follows VPCC,R ,VPCC,I
2
r=
Eq. (7) can be split in its real and imaginary parts according to
Re{f m V sub g m } b1 = , Re{g m }
1
(7)
gm
b
Fig. 5. Change of coordinate frame.
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
75
Table 1 Data of the 132/20 kV–24 MVA transformer at the HV/MV substation Type of windings
Ratio for a = 1
Ratio for amin
Ratio for amax
xsub [p.u.]
OLTC positions
Yg
130/20
0.90
1.05
0.08
16
To obtain the optimal voltage V opt , the value of ıopt is directly substituted into the following expression V opt = VPCC,R + jV PCC,I =
b
1
2
+ r cos ıopt
+j
b
2
2
+ r sin ıopt
(16)
Then, the optimal set point Qopt is evaluated by substituting V opt into (9) in place of V PCC . Finally, Qopt must be checked with respect to the allowable range of DER reactive power and, then, sent to the classical reactive power control scheme.
Table 2 Data for both the 20 kV feeders. Line name
Rli []
Xli []
l1 l2 l3 l4 l5 l6 l7 l8
0.34215 0.34215 0.34215 0.34215 0.2281 0.2281 0.2281 0.2281
0.4806 0.4806 0.4806 0.4806 0.3204 0.3204 0.3204 0.3204
3.4. Case of multiple DERs
4. Case studies
The OS design has been developed assuming a single DER along a feeder. In the following some considerations are reported about applying the proposed OS design to the general case of the distribution system shown in Fig. 2 with multiple DERs. First of all, let the case of two DERs installed on two different feeders be considered. Since the voltage at the MV busbar is roughly kept constant by the OLTC action, the power losses along each feeder cannot be significantly affected by the reactive power of the DER installed on the other feeder. Then, DERs on different feeders can be equipped with the OS. In the case of OLTC equipped with LDC, the above consideration is still standing provided that the OS of each DER minimizes the losses along its feeder starting from the node j + 1, being the jth node the last node along the feeder included in the LDC, see (3). A further consideration concerns the case of multiple DERs along the same feeder. In the assumption of avoiding any on-line coordination, only one DER for each feeder can be equipped with the proposed OS. The best candidate is the DER with the highest impact of the feeder power losses and it is identified taking into account both its size and location. The presence of other DERs along the same feeder introduces modeling inaccuracies in the OS design. However, it is possible that different DERs are “electrically distant”. It is the case of some actual feeders along which it is possible to identify some areas with the following characteristics: each area represents a group of nodes whose voltages are strictly coupled and different areas are connected one to another by long distance conductors. In this case one DER for each area can be equipped with the OS while still avoiding any on-line coordination. To identify such areas, some methods presented in literature can be used: in [17] “zones of influence” are identified applying -decomposition [18] to a voltage sensitivity matrix, whereas in [19,20] “voltage load areas” are obtained by a method based on the inherent structure theory of the networks [21,22] applied to the nodal admittance matrix. For each area, the DER which is the best candidate to be equipped with the OS is chosen accounting for both its size and location and its OS minimizes the power losses in the area. In conclusion, the proposed approach, on one side, cannot guarantee the overall loss minimization that can be obtained by acting on all the DERs installed along a feeder, but, on the other side, achieves the best solution that can be reached without additional measurement and communication systems. For this reason, the proposed OS is attractive to improve the performance of present-day distribution systems, postponing the large investments required by the future smart grids.
Reference is made to the 20 kV–50 Hz distribution system shown in Fig. 6, which includes distributed generators as DERs. Two feeders are supplied by a 24 MVA HV/MV transformer which is equipped with an OLTC regulating the voltage of the MV busbar at 1.02 p.u.; the characteristics of the transformer are reported in Table 1. For both the feeders the electric characteristics are reported in Tables 2 and 3. The feeder # 1 includes a 2.0 MW wind DG with OS at node 4 and a 1.0 MW PhotoVoltaic (PV) DG without OS at node 7. Concerning the wind DG, its reactive power injection is limited to ±1.71 MVAr; the rated wind speed is 12 m/s. Concerning the 1.0 MW PV DG, it operates at its rated power and with unity power factor. The feeder # 2 includes a 1.4 MW PV DG at busbar 7 and operates at 100%; it is equipped with OS and its reactive power injection is limited to ±0.85 MVAr. The distribution system has been simulated using PSCAD/EMTDC. 4.1. Steady-state performance In this section the results in terms of steady-state accuracy of the proposed OS are analyzed. To this aim, it is assumed that the wind speed is constant at 12 m/s. The results related to three cases are reported. In the case A, the feeder # 1 operates at full loading conditions whereas the feeder # 2 at half loading conditions. In the case B, the feeder # 1 operates at half loading conditions whereas the feeder # 2 at low loading conditions equal to 25% of the peak load. Finally, in the case C, the same total load as the one assumed in case B is considered but its sharing among the nodes is different. This latter case is useful to analyze the effects of the errors of the load factors on the OS performance. In fact, in the OS development, the load factors are assumed to be known. Their values are derived from historical records of measurements and/or from the load rated powers. Indeed, during operation, the load factors are subject to variations. While their Table 3 Peak loads and rated load factors. Load name
PLi [kW]
L1 L2 L3 L4 L5 L6 L7 L8
156.5 156.5 136.25 136.25 684.25 684.25 1229.0 1229.0
QLi [kVAr] 76.5 76.5 66.675 66.675 334.5 334.5 600.925 600,925
kLr
i
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
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Fig. 6. Simulated distribution system with two feeders and three DGs.
Table 4 Rated versus modified load factors, case C. Feeder # 1
Feeder # 2 kLr
Load
Modified kLi
i
L1 L2 L3 L4 L5 L6 L7 L8
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
kLi −0.0297 −0.0445 −0.0148 0.0297 0.0594 0.0297 −0.0075 −0.0223
0.0652 0.0800 0.0457 0.0012 0.0957 0.1254 0.2860 0.3008
structural variations can be taken into account by using different look-up tables, they are always subject to intrinsic uncertainties due to random load changes. To account for these latter uncertainties, in case C the values of the load factors are significantly changed with respect to the rated ones, by increasing and decreasing the loads in both the feeders. The modified values kLi are reported in Table 4. For the sake of comparison, in Table 4 are also reported the rated values kLr and the differences kLi between the rated and the
Load L1 L2 L3 L4 L5 L6 L7 L8
kLr
i
0.0355 0.0355 0.0309 0.0309 0.1551 0.1551 0.2785 0.2785
Modified kLi
kLi −0.0223 0.0297 −0.0074 0.0297 −0.0297 −0.0371 −0.0223 0.0594
0.0578 0.0058 0.0383 0.0012 0.1848 0.1922 0.3008 0.2191
Table 6 DG reactive powers and total feeder losses, case B. Control type
OS ORPF UPFC
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
1.36 1.14 0.0
0.39 0.50 0.0
5.6 5.4 10.8
[kW]
i
modified values. For each feeder, the performance of the OSs is compared with the one obtained by a classical control scheme in which the setpoints are fixed; in particular a Unity Power Factor Control (UPFC) is considered. Moreover, the OS performance is compared also with an optimization benchmark. To this aim, a classical Optimal Reactive Power Flow (ORPF) algorithm has been run for the two cases, minimizing the losses on both feeders and assuming the same values of the loads and of the active power injections of the DGs as the ones used in the numerical simulations. In Tables 5–7 the values of the reactive powers of the two DGs with OS and of the total losses along the feeders are reported and
compared with the corresponding values obtained by the UPFC and by the off-line benchmark ORPF, referring respectively to the cases A, B and C. In general, the results show that the OS presents a performance which is very close to the benchmark obtained by the off-line ORPF. In the case A, the values of QPCC are the same with both OS and ORFC because each DG saturates its reactive power injection. In the case B, due to the approximations introduced in the modeling when multiple DERs are present, the OS does not reach the exact optimum represented by the ORPF solution; nevertheless the
Table 5 DG reactive powers and total feeder losses, case A.
Table 7 DG reactive powers and total feeder losses, case C.
Control type
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
OS ORPF UPFC
1.71 1.71 0.0
0.85 0.85 0.0
25.5 25.5 43.7
Control type
Feeder # 1 QPCC [MVAr]
Feeder # 2 QPCC [MVAr]
Total feeders losses
OS ORPF UPFC
0.79 1.08 0.0
0.47 0.49 0.0
6.3 6.0 11.1
[kW]
[kW]
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
77
Fig. 7. Total losses along the feeders versus the average variation of the load factors.
difference in terms of active power losses between the OS and the ORPF is quite limited. In the case C, the OS operates using the rated values kLr . Then, an i
error is introduced in the evaluation of the optimal set-point. From the analysis of Tables 5–7 it is apparent that the results obtained by OS are still good when compared with the ORPF benchmark. It is due to the small sensitivity of the optimal set point to the variations of the load factors, as it is evident comparing the results with the ones in case B. In all the considered cases, the reduction of losses achieved by OS compared to the classical UPFC control is significant and it is obtained by simply making smarter the local reactive set-point design. For the sake of completeness, a sensitivity analysis of the OS performance to the errors on the load factors has been performed. To this aim, while the total load has been kept equal to the one of case B, the load sharing among the nodes has been varied yielding different sets of kLi . Each set is characterized by a value k equal to n r 1 |kLi − kLi | 100 r n kL
k =
i=1
i
which is the average value of the relative variations of kLi with respect to the rated values kLr . In Fig. 7 the values of the total power
Fig. 8. Time evolution of the wind DG injected powers (PPCC , QPCC ), and of the voltages (V0 , V4 , V8 ) for feeder #1 in case B with wind speed variations.
The results of a 20 simulation are reported in Fig. 8, showing the time evolution of the injected powers PPCC and QPCC of the wind DG and of the voltage amplitudes V0 , V4 and V8 of feeder # 1 in the case B. The OS is initialized with QPCC at its maximum value (1.71 MVAr). At about t = 1 the OS starts working, corrects the optimal set-point and decreases QPCC . During the subsequent transient, also the OLTC varies its operating conditions (see V0 ). Between t = 1 and t = 3 .5 there is also a steep increase of PPCC due to wind speed variation. Consequently, the OS changes the reactive power injection, increasing its value so as to reduce losses. After t = 3 .5 , PPCC is subject to some slower variations, which are tracked by the OS by varying consequently QPCC . The effects of these active and reactive power injections on the voltage profile along the feeder # 1 are also evident in Fig. 8; as expected, the voltage V0 is quite constant whereas the voltages V4 and V8 are subject to larger variations.
i
losses along the feeders Ploss versus k are reported with reference to the OS and the ORPF. The ORPF uses the actual load factors and can be thus assumed as the benchmark. The OS uses the rated values kLr and consequently evaluates a sub-optimal solution. Anyway, i
analyzing Fig. 7, the robustness of the OS is quite evident even in presence of huge errors on the values of the load factors. In particular, for a value of k equal to about 90% the resulting error on the power losses is equal to 1.5%. 4.2. Dynamic performance In actual applications, the wind DG does not operate with constant wind speed but it is subject to random variations of the energy source, which cause changes of the injected active power. Then, in this subsection it is tested the ability of the OS to track the optimal set-point in presence of such random variations. Numerical simulation have been performed with reference to the case B, as defined in the previous section. The time evolution of the wind speed has been obtained by combining the effects of the variation of its mean value with a noise. The former variation is obtained from actual measurements [23], whereas the noise is obtained by using the wind gust model available from PSCAD library.
5. Conclusion In this paper a new reactive power control scheme for DERs has been proposed so as to minimize the power losses in a smart distribution grid. The classical DER reactive power control scheme has been enriched by an on-line Optimization Strategy, whose strong points are: to keep the classical structure of a DER control system, to use only local measurements of voltage and current at the PCC, to account for the changes of the operating conditions of the distribution system, to limit on-line data exchange with the HV/MV substation to the only case of significant changes of the distribution system structure and to avoid any data exchange with other DERs. The only drawback is related to the modelling approximations that are introduced in presence of multiple DERs and that cause inaccuracies in the output of the Optimization Strategy. Numerical simulation results have evidenced the improvements of the performance by adopting the proposed Optimization Strategy, which proved to give suboptimal results very close to the optimal ones. Acknowledgment The authors acknowledge the financial support to this research by GETRA S.p.A.
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A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
Appendix A.
In a similar way, by substituting into (3) the constraint (6), VCs can be expressed as function of V i as
The nodal voltage V PCC at PCC node can be expressed as function of either the Thevenin equivalent parameters
V m ≤ |V i = i V sub + ˛i V PCC | ≤ V M
V PCC = V eq + Z eq I PCC
(A.1)
V PCC = f m V sub + g m I PCC
(A.2)
Comparing Eqs. (A.1) and (A.2), it derives fm =
V eq
(A.3)
By substituting into (2) and (4) the expression of I PCC derived from (A.1) it is obtained V i = f i V sub + g i
V PCC − V eq
i = 1, . . ., n
Z eq
PPCC − jQPCC = V PCC
(A.4)
gif m gm
V PCC − V eq
where c1i , . . ., c4i for i = 1, . . ., n are equal to
c2i = 2(Re{i V sub }Re{˛i } + Im{i V sub }Im{˛i })
(B.10)
c3i = 2(−Re{i V sub }Im{˛i } + Im{i V sub }Re{˛i })
(B.11)
c4i = (i V sub )
(A.5)
Z eq
V i = i V sub + ˛i V PCC
gi gm
i = 1, . . ., n
(A.6)
i = 1, . . ., n
(A.7)
2 −f V VPCC m sub V PCC
(A.8)
gm
Appendix B. The objective function J can be expressed as function of V i by substituting into (3) the expression of the PF constraint given by (6) J=
Rli Rl2 + Xl2
i=1
i
(i V sub + ˛i V PCC − i−1 V sub − ˛i−1 V PCC )
2
(B.1)
i
Then, being V sub , i and ˛i known once V eq and Z eq are estimated, J can be rewritten as function of VPCC,R and VPCC,I as follows J=
n
2 a1 VPCC,R
2
VPCC,R =
b1 + cos ı 2
(C.1)
VPCC,I =
b2 + sin ı 2
(C.2)
2 + a1 VPCC,I
+ a2 VPCC,R + a3 VPCC,I + a4
By substituting Eqs. (C.1) and (C.2) into (10)–(12), the expression of J, PF and VCs are replaced by J = d1 cos ı + d2 sin ı + d3 2 + d4
(C.3)
=r
(C.4)
Vm ≤
d1i cos ı + d2i sin ı + d3i + d4i ≤ V M
d1 = a1 b1 + a2
(C.6)
d2 = a1 b2 + a3
(C.7)
d3 = a1
(C.8)
d4 = a1
b21 4
(B.2)
where a1 =
i=1
Rli Rl2 + Xl2 i
i=1
2
+
i=1
a4 =
i=1
Re{V sub (˛i − ˛i−1 ) (i − i−1 )} 2
Rl2 + Xl i
Rli
+ a2
b1 b2 + a3 + a4 2 2
Rli Rl2 + Xl2
(C.10)
d2i = c1i b2 + c3i
b2 2
(C.11)
i
2
(C.12) b21 4
+ c1i
b22 4
+ c4
(C.13)
Substituting the constraint (C.4) into (C.3), the J changes into (B.5)
i
2 Vsub (˛i − ˛i−1 )
(C.9)
b1 2
d4i = c1i
i
i
4
d1i = c1i b1 + c2i
(B.4)
i
Im{V sub (˛i − ˛i−1 ) (i − i−1 )} 2
Rl2 + Xl
n
(B.3)
b2
d3i = c1i
Rli
n
a3 = 2
2
i
n
a2 = 2
(˛i − ˛i−1 )
i = 1, . . ., n (C.5)
where
i=1
n
(B.12)
Appendix C.
yields
n
(B.9)
The cartesian coordinates VPCC,R and VPCC,I in the polar plan are expressed as
˛i =
PPCC − jQPCC =
2 2 c1i VPCC,R + c1i VPCC,I + c2i VPCC,R + c3i VPCC,I + c4i ≤ V M (B.8)
for i = 1, . . ., n.
Finally, imposing i = fi −
c1i = ˛2i
g m = Z eq
V sub
(B.7)
and, then, rewritten in terms of VPCC,R and VPCC,I as Vm ≤
or the electric circuit parameters
i = 1, . . ., n
J = a cos ı + b sin ı + c
(C.14)
with a = rd1 , b = rd2 , c = r2 d3 + d4 . In a similar way, the VCs in (C.5) becomes (B.6)
Vm ≤
di cos ı + ei sin ı + fi ≤ V M
i = 1, . . ., n
(C.15)
A.R. Di Fazio et al. / Electric Power Systems Research 109 (2014) 71–79
with di = rd1i , ei = rd2i , fi = rd3i + d4i . To rewritten the box constraints (C.15) in terms of ım ≤ ı ≤ ıM
(C.16) Vm
VM
the boundary values and are mapped into the variable ı, by calculating the closed-form analytic solution ılim of the following i equation once for Vlim = Vm and then for Vlim = VM 2 di cos ılim + ei sin ılim + fi = Vlim i i
i = 1, . . ., n
(C.17)
It yields n values ım and ıM for both the minimum and maximum i i values of ı. The boundary values ım and ıM are trivially evaluated } and the min{ıM } respectively. as the max{ım i i References [1] A. Yazdani, A.R. Di Fazio, H. Ghoddami, M. Russo, M. Kazerani, J. Jatskevich, K. Strunz, S. Leva, J. Martinez, Modeling guidelines and a benchmark for power system simulation studies of three-phase single-stage photovoltaic systems, IEEE Trans. Power Deliv. 26 (2) (2011) 1247–1264. [2] J.H. Laks, L.Y. Pao, A.D. Wright, Control of wind turbines: past, present, and future, in: American Control Conference ACC’09, 2009, pp. 2096–2103. [3] M.H. Nehrir, C. Wang, K. Strunz, H. Aki, R. Ramakumar, J. Bing, Z. Miao, Z. Salameh, A review of hybrid renewable/alternative energy systems for electric power generation: configurations, control, and applications, IEEE Trans. Sustain. Energy 2 (4) (2011) 392–403. [4] T.W. Eberly, R.C. Schaefer, Voltage versus var/power-factor regulation on synchronous generators, IEEE Trans. Ind. Appl. 38 (6) (2002) 1682–1687. [5] P. Vovos, A. Kiprakis, A. Wallace, G. Harrison, Centralized and distributed voltage control: impact on distributed generation penetration, IEEE Trans. Power Syst. 22 (1) (2007) 476–483. [6] A. Aquino-Lugo, R. Klump, T. Overbye, A control framework for the smart grid for voltage support using agent-based technologies, IEEE Trans. Smart Grid 2 (1) (2011) 173–180. [7] P. Carvalho, P. Correia, L. Ferreira, Distributed reactive power generation control for voltage rise mitigation in distribution networks, IEEE Trans. Power Syst. 23 (2) (2008) 766–772.
79
[8] K. Tanaka, M. Oshiro, S. Toma, A. Yona, T. Senjyu, T. Funabashi, C.-H. Kim, Decentralised control of voltage in distribution systems by distributed generators, IEE Proc. Generat. Transm. Distrib. 4 (11) (2010) 1251–1260. [9] H.E. Farag, E.F. El-Saadany, R. Seethapathy, A two ways communication-based distributed control for voltage regulation in smart distribution feeders, IEEE Trans. Smart Grid 3 (1) (2012) 271–281. [10] A.R. Di Fazio, G. Fusco, M. Russo, Optimisation strategy applied to DG reactive power for decentralised voltage control in smart grids, in: Cigrè International Symposium, The Electric Power System of the Future, Bologna, Italy, 2011. [11] A.R. Di Fazio, G. Fusco, M. Russo, Decentralised voltage regulation in smart grids using reactive power from renewable DG, in: IEEE International Energy Conference & Exhibition ENERGYCON 2012, Florence, Italy, 2012. [12] I.D.P.W.G. Report, Radial distribution test feeders, IEEE Trans. Power Syst. 6 (3) (1991) 975–985. [13] W.H. Kersting, Distribution System Modeling and Analysis, CRC Press LLC, Boca Raton, Florida, USA, 2002. [14] G. Fusco, A. Losi, M. Russo, Constrained least squares methods for parameter tracking of power system steady-state equivalent circuits, IEEE Trans. Power Deliv. 15 (3) (2000) 1073–1080. [15] G. Fusco, M. Russo, Adaptive Voltage Control in Power Systems – Modeling, Design and Applications, Advances in Industrial Control, Springer, London, UK, 2007. [16] K. Rogers, R. Klump, H. Khurana, A. Aquino-Lugo, T. Overbye, An authenticated control framework for distributed voltage support on the smart grid, IEEE Trans. Smart Grid 1 (1) (2010) 40–47. [17] L. Yu, D. Czarkowski, F. de León, Optimal distributed voltage regulation for secondary networks with DGs, IEEE Trans. Smart Grid 3 (2) (2012) 959–967. ˇ [18] D.D. Siljak, Decentralized Control of Complex Systems, Mathematics in Science and Engineering, vol. 184, Academic Press, San Diego, CA, 1991. [19] G. Valtorta, et al., Prototypes and algorithms for network management, providing the signals sent by the DSOs to the aggregators and the markets, enabling and exploiting active demand, Deliverable D3.1, ADDRESS Consortium EU-FP7, 2011 http://www.addressfp7.org [20] G.M. Casolino, A.R. Di Fazio, A. Losi, M. Russo, Smart modelling and tools for distribution system management and operation, in: IEEE International Energy Conference & Exhibition ENERGYCON 2012, Florence, Italy, 2012. [21] M.A. Laughton, M.A. El-Iskandarani, The structure of power network voltage profiles, in: 7th Power Systems Computation Conference PSCC, Lausanne, Switzerland, 1982, pp. 845–851. [22] G. Carpinelli, A. Russo, M. Russo, P. Verde, Inherent structure theory of networks and power system harmonics, IEE Proceedings on Generation–Transmission & Distribution 145 (2) (1998) 123–132. [23] NREL, MDIC/SRRL base line measurement system (December 2011). http://www.nrel.gov/midc/srrl bms