Optimal voltage control strategies for day-ahead active distribution network operation

Electric Power Systems Research 127 (2015) 41–52

Contents lists available at ScienceDirect

Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Optimal voltage control strategies for day-ahead active distribution network operation M.Z. Degefa a,∗ , M. Lehtonen a , R.J. Millar a , A. Alahäivälä a , E. Saarijärvi b a b

Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland Trimble, Espoo, Finland

a r t i c l e

i n f o

Article history: Received 6 March 2015 Received in revised form 21 May 2015 Accepted 23 May 2015 Keywords: Active network management Distributed generation (DG) Dynamic thermal rating (DTR) Onload tap changer (OLTC) State estimation Voltage control

a b s t r a c t The aim of this study is to develop a coordinated day-ahead voltage control strategy for an active distribution network. A framework comprising a synergy of real-time dynamic thermal rating (DTR) and coordinated voltage control (CVC) is proposed for solving the voltage quality and thermal limit problems associated with a high penetration level of distributed generation (DG) in an active distribution network. The CVC scheme involves solutions such as On-Load-Tap-Changers (OLTCs), active and reactive power control of DG units, and switchable shunt VAR compensation devices (SVCs). Loss minimization and voltage penalty objective functions in the CVC optimization problem are compared. A 147 bus test distribution network planned for an actual geographical location is used to evaluate the proposed DTR-based day-ahead CVC strategy. In this study, we have showed that the reactive power absorption/injection potential of DG units can play an important role in CVC. Moreover, the study demonstrates that real-time thermal rating boosts the utilization of reactive power resources in the distribution system. Finally, the study investigates the practicality of day-ahead active distribution network operation planning for CVC. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In today’s active distribution network there is an ever increasing penetration level of distributed generation (DG) driven by technical and policy forces. Among the various limiting factors inhibiting the further installations of DG units are feeder thermal capacity limits and the steady state voltage rise problem [1]. With regard to dealing with the voltage rise problem, reactive power contribution by DG units is one of the most commonly proposed approaches [2]. Wind turbines, for instance, by virtue of their power electronic converters, are able to control active and reactive power independently [3]. The voltage source inverter in PVs is also an interface that enables the control of reactive power. These non-dispatchable DG units, such as PV and wind, operate a significant fraction of their time much below their rated power, during which they can provide reactive power service. Nevertheless, the present grid code, for example in Finland, does not allow distributed generation to participate in distribution network voltage control in any way. Moreover, the currently used distribution network planning tools and procedures are not capable of taking active voltage control into account, as discussed in [4]. There are

∗ Corresponding author. Tel.: +358 44 5654598; fax: +358 9 470 2991. E-mail address: merkebu.degefa@aalto.fi (M.Z. Degefa). http://dx.doi.org/10.1016/j.epsr.2015.05.018 0378-7796/© 2015 Elsevier B.V. All rights reserved.

two possible explanations for the lack of a collective agreement on deploying DG units for voltage control in a distribution network. The first is the insufficient measurements and consequently the limited state estimation services in distribution networks. The second reason could be the absence of power flow constraints such as bottlenecks in many existing under-loaded distribution networks, which tends to have inhibited the deployment of realtime line and cable rating programs. Given the rapid development of active distribution networks, both aforementioned reasons are becoming obsolete. With the installation of automatic meter reading (AMR) devices, the accessibility of distribution network data has significantly increased in terms of resolution as well as clarity. Contradicting the second reason, the increasing installations of DG units are creating voltage level and capacity limit problems in today’s distribution network. Hence, broad studies, with dependable control mechanisms for the coordinated operation of various types of voltage regulating options including DG units, are required. In addition, the formulation for the multi-objective optimization with coordinated voltage control involving DG units needs to be understandable and economical. An effective methodology for multi-objective DG operation for distribution system volt/var control during normal and emergency situation is therefore vital. There have been numerous studies solving optimization problems for coordinated voltage control in distribution systems. Some

42

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

studies considered the coordination of only two voltage control methods, while others investigated all the available methods, including the reactive power control of DG units. The study in [5] presents a coordination of OLTC and Static-var-Compensators (SVC) in an unbalanced distribution system. The proposed approach is a two-stage decision making procedure, where in stage one, an optimization problem of loss minimization is solved and in stage two, the minimization of switching due to economic and technical considerations is solved. Nevertheless, in [5] the DG units have been assumed to operate with unity power factor; no reactive power supply is considered from the DG units. In [6], coordination among multiple SVCs, OLTC and DG units is presented for an online voltage control in distribution systems. The synchronous machine-based renewable DG units are also involved in the voltage regulation, which minimized, according to [6], the total tap operation of SVRs. The method in [6] uses pseudo measurements for load and DG generation; however, it doesn’t include the uncertainties involved with the measurements or uncertainties in the voltages from distribution state estimation. The study in [7] proposes a hierarchical rule based coordinated voltage control strategy involving OLTCs and DG units. In mitigating voltage problems, predefined steps tap changing steps, Q regulation of DG units and PQ regulation of DG units are initiated sequentially until the problem is alleviated. In the studies [4,8], the authors presented a method to enable distribution system operators to integrate the voltage level management potential of DG units in their network operation and planning principles. These studies are efforts to relate the vast optimization and rule-based coordinated voltage control theoretical studies to the practical conditions of the existing network. In [8], a planning procedure is proposed so that implementation in the currently used network planning tools is convenient. The coordination between substation voltage and DG reactive power is claimed to be the least cost method in [4], which used statistical distribution planning to select voltage control strategy. In the statistical planning, one year load and production curves were used to conduct load flows which can then be used to evaluate the costs of different control strategies [4]. Nevertheless, the rule-based procedures in [4,8] do not investigate the costs of the optimal coordination of different voltage control strategies. A comprehensive voltage control strategy among OLTCs, substation switched capacitors and feeder-switched capacitors is presented in [9]. The study also investigated the impact of DG units on the control strategies, in which they found that a constant voltage operation of DG units is beneficial for a significant reduction in OLTC operation. In [9], however, the DG is set to generate constant active power, which is not possible in the case of PVs and Wind, ruling out the possibility of PQ control of DG. The study in [10] proposes a simple DG local reactive power control with occasional communication with distribution network operators (DNO). The proposed approach aims to guarantee that active power generation does not cause voltage rise. With an objective function that minimizes DG curtailment and voltage violations, the study in [11] proposes a comprehensive centralized voltage constraint management approach. Provided that the VCM problems are formulated properly, the MINLP solvers generally provide an acceptably fast solution, as most distribution systems are equipped with a relatively small number of discrete control means [11]. In [11], the transfer of DG between feeders using only remotely controlled switches only occurs when the DG curtailment cost exceeds the cost of switching. There are only a few studies (such as [12,13]) which tackle the real-time management of voltage and thermal constraints local to DG connection. The decentralized approach in [12] aims to avoid extensive sensing and communications, where the thermal constraint is managed by setting a constant line capacity threshold which triggers the trimming of wind generation if violated.

A centralized management of thermal constraints, while inhibiting violation of voltage limits, is presented in [13] by employing remotely controlled switches to reduce the DG curtailment. The study claims that the additional degree of freedom provided by remotely controlled network switches leads to less DG curtailment. However, as in [12], in [13] the thermal limits of all lines are set to a constant value. In practice, both the capacity threshold and DG generation fluctuates a lot, following weather variations in real-time. Hence, dynamic thermal rating is proposed in this study to manage voltage level and network losses while the real-time line thermal limit is being respected in the constraint. In addition, in this study OLTCs, DG units and SVCs are coordinated in addressing the voltage and thermal constraints in an active distribution network. The purpose of this study is to provide a CVC strategy for the day-ahead operation of an active distribution network with updated network capacity using real-time thermal rating (RTTR). The CVC involves tap changing transformers, switchable static VAR compensators and DG units. The day-ahead control strategies use day-ahead forecasts of load, weather variables and DG generation. Voltage penalty function and network loss minimization objectives are compared in solving the CVC problem involving DG units. The limitations of the method proposed in this study are mostly associated with uncertainties in load and weather variable forecasts. Further, the execution complexity due to inconsistencies between the planned day-ahead settings of voltage control devices and their intraday local measurement-based closed loop operation pose a challenge. Nevertheless, with the development of network operation planning from day-ahead to hour- and minute-ahead planning, the inaccuracies are likely to become less significant. Section 2 reviews the various voltage regulating mechanisms and discusses the reactive power potential of DG. In Section 3, a brief discussion of the real-time thermal rating (RTTR) method employed in this study is presented. The subsequent section, Section 4, presents the CVC formulation, which incorporates the DG Q/V droop control variables and network component ratings. In this section, the loss minimization and voltage deviation penalty function based objectives are also discussed. In Section 5, the test active distribution network and the load and weather variables utilized in the analysis are presented. Section 5 also discusses the main observations of the analysis while Section 6 briefly discusses practical concerns related to communicating control set-points. The last section, Section 7, summarizes the main findings of this study. 2. Voltage control methods There are two typical voltage level problems in distribution systems. The short-term problem, which lasts for not more than a minute, and the long-term problem, where the voltage level remains outside the ±10% limit for more than 1 min. Over voltage and under voltage events require proper management that utilizes the dependencies of voltage and other variables, such as active and reactive load and generation, as shown in Fig. 1 and (1). The voltage at busbar 2 in Fig. 1 can be approximated as V2 ≈ V1 +

R (PG − PL ) + (±QG − QL ± QC ) X V2

(1)

Fig. 1. A simple illustration of voltage dependency in distribution network [14].

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

43

where PG and QG are local generation connected with local load PL , and QL and QC are supplied from a reactive compensator. 2.1. Distribution system voltage regulation devices 2.1.1. On-load tap-changers (OLTCs) An OLTC is a transformer component controlled automatically by a relay to increase or decrease voltage by altering the tap position of the transformer [14]. Usually, OLTCs operate following the connection point voltage level as a feedback control loop. In a CVC scheme, however, the operation of OLTCs might be needed for correcting voltage level problems elsewhere in the distribution network. The CVC scheme, therefore, needs to communicate the optimized set-points for the OLTCs. Nevertheless, the OLTCs might also need to take corrective actions for local contingencies without waiting for the centrally running optimization. Hence, an intelligent OLTC operating with two layers of control regimes, central and local, is the solution. This control scheme is presented briefly in Section 6. Nevertheless, in the test case, OLTCs receiving only centrally optimized set-points are considered. The OLTCs are mainly installed in the HV/MV primary substation transformer. Nevertheless, their installation in the MV/LV secondary substation has been recommended to abet the voltage problem introduced by DG units, as in [15]. In this study, the optimal placement or optimal OLTC installation problems are not discussed. However, with a given OLTC installation level and without further device investment, we attempt to improve voltage quality through CVC, involving DG units and an RTTR system. 2.1.2. Switchable static VAR compensation devices (SVC) An SVC is a shunt-connected static var generator or sink whose output is adjusted to exchange capacitive or inductive current. Hence, SVCs are capable of either supplying or absorbing reactive power. The response time of SVCs is also fast enough to respond to transitional voltage fluctuations. In this study, the SVCs comprise either thyristor-switched capacitors or reactors. 2.1.3. DG reactive power control methods The reactive power capability of DG units (wind turbines and solar PVs in this study) originates from their inverter circuits connecting to the grid. Except for limiting the maximum reactive power intake or supply, the active power generated does not have an impact on the reactive power capacity of DG units, as formulated in (2). This fact enables solar PVs to be utilized in reactive power balance, even during night time when no generation is possible. The inverter apparent power rating, however, sets the absolute possible reactive power capacity, as shown in (2) and Fig. 2.

 Qmax (t) =

2 Smax − Pact (t)2

(2)

where Smax (red line in Fig. 2) is the inverter apparent power rating, Pact (t) is the actual active power generated by DG at time t (green line in Fig. 2) and Qmax (t) is the corresponding maximum reactive power supply or intake capability. Standards such as IEEE 1547 do not currently allow active voltage regulation by DG inverters at the point of common coupling (PCC) to access maximum amount of real power and to avoid unnecessary interaction among voltage controllers. Otherwise, there is no other technical limitation inhibiting the usage of reactive power of DG units. Many inverters have the capability of providing reactive power to the grid. Inverters can also be oversized just to increase the capacity of their reactive power balance.

Fig. 2. Inverter reactive power capability curve. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

In a highly resistive network, such as a low voltage distribution network, the voltage is more dependent on active power than reactive power. Conversely, when the reactance of a power system network is more significant than the resistance the voltage will be more sensitive to changes in reactive power. Hence, in the former scenario a P/V droop controller is recommended and in the latter case a Q/V droop controller would be more effective. DG control for voltage regulation involves either soft or hard curtailment. With hard curtailment, we disconnect the DG altogether. However, with soft curtailment either of the P/V or Q/V droop control methods can be utilized. 2.1.3.1. Q/V droop controller. This type of control is also called voltage dependent reactive power control. The DG units considered in this study are PVs and wind turbines. The Q/V droop method does not need a source of real power for generating the necessary reactive power for compensation. Since the main objective of PV generators is to produce active power, their reactive power is limited to the maximum apparent capacity of the inverter.

Q =

⎧ V ⎪   · Qmax , V < 0.9 or V > 1.1 ⎪ ⎪ ⎪ V  ⎪ ⎪ ⎪ ⎪ ⎨ 0, 1 − D ≤ V ≤ 1 + D Q

max (−V + 1 + D) , 1 + D < V ≤ 1.1 ⎪ ⎪ 0.1 − D ⎪ ⎪ ⎪ ⎪  ⎪ ⎪ ⎩ Qmax −V + 1 − D , 0.9 ≤ V < 1 − D

(3)

0.1 − D

Qmax = P × tan (acos (PFlim ))

(4)

where the power factor limit is PFlim and the deadband range setting value is D. The graphical presentation of (3) and (4) is presented in Fig. 3.

Fig. 3. Q/V control with dead-band.

44

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

2.1.3.2. DG P/V droop controller. The P/V droop can be implemented with either soft curtailment in the case of dispatchable DG or disconnection of the DG altogether in the case of non-dispatchable DG. The P/V droop controllers are effective in resistive networks. Both the P/V and Q/V -control could be a constant droop or with a deadband. In this way, the DG units would only react to voltages that exceed a certain threshold voltage. In the P/V droop control, the DG units contribute to the load sharing, depending on both their ratings (droops) and the line impedances. The P/V droop control strategy is based on the formulation shown in the following equation:



Pi =



Pmax,i − ki Vi − Vcrit,i



Pmax,i

∀Vi ≥ Vcrit,i ∀Vi < Vcrit,i

(5)

where Vcrit,i is the voltage above which the power injected by the DG is decreased with the droop coefficient ki and Pmax,i is the nominal power or the maximum power available by the DG. Vi and Pi are the voltage level and DG output at node i. The P/V droop equation in (5), hence, executes the active power curtailment required for keeping the bus voltage within an acceptable range. In this study, the Q/V droop controller method with dead-band is used to control the reactive power supply or intake of DG units. 3. Real-time thermal rating Static distribution network ratings are usually calculated assuming conservative weather conditions. For example, the rating of overhead lines is calculated under low wind speed conditions and high ambient temperature. These ratings are usually provided seasonally and are fixed within the season. The RTTR method, however, estimates the real-time thermal states and provides hour ahead ratings, for example, by using the previous loading conditions and local weather measurements or forecasts. The weather variables relevant to the thermal ratings are wind speed, ambient temperature, solar irradiation and ground soil temperature. The emerging active distribution network is facing distributed generation and demand response induced stochastic loading characteristics. Hence, to implement the real-time monitoring and operation of an active distribution network, a real-time thermal rating system is essential. The RTTR system requires dynamic thermal models of the essential components such as underground cables, overhead lines and substation transformers. Thermal models are expected to be capable of giving the maximum next hour carrying capacities by using the current thermal state information and forecasts of weather variables. The equivalent ladder network circuit of underground cables installed in unfilled conduit is presented in Fig. 4. It shows the thermal resistances and thermal capacitances emulating the transient thermal responses. IEEE Std. 738 and IEEE Std. C57.91 loading guidelines for overhead conductors and oil-immersed transformers

Fig. 4. A seven loop thermal model for an underground cable inside an unfilled conduit.

are used in the RTTR system. The underground cable thermal model developed by the authors and the implementation procedures of the RTTR system are detailed in [16,17]. 4. Optimal day ahead CVC formulation The main goal of CVC in distribution networks is to compensate for the load and DG generation variations so that the customer supply voltages are kept within certain bounds. The utilization of DG units coordinating with SVCs and OLTCs for voltage control can impose higher loading on the network. In other words, to tap the supply and absorption capacity of reactive power in a distribution system the lines and cables are required to cope with increased loading. The network loading capacity in a static rating regime, however, is heavily limited compared to real-time thermal rating. The day-ahead CVC framework presented in Fig. 5 comprises weather variable and load forecasts. The DG output forecast is based on the weather variables, while the component ratings depend on both the weather variables and forecasted loading. The errors in the forecasting will in fact be carried through to the CVC settings. Hence, evaluating the uncertainties in the control settings is also equally crucial. Besides, while being the general day-ahead guideline for the voltage regulating devices, the optimal control settings from the proposed framework require updates within each day. In this study we mainly focus on providing the optimal CVC set-points for day-ahead distribution network operation. Practical matters, such as communication, uncertainties and contingencies are briefly discussed in Section 6 from the multi-agent system perspective. In the optimal decision of set-points for CVC, the ratings of components such as lines and cables must be considered. However, these capacity limits could either be set based on static rating principles or real-time thermal rating methods. The incorporation of an RTTR system with CVC brings two main benefits: the first

Fig. 5. Three level CVC strategy procedure.

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

45

is the lower cost of operation of a facility involved in CVC and the second is a higher utilization and integration potential of DG units.

4.1. Objective functions Defining an objective function to maintain power quality and reduce losses is a challenge. For loss minimization, the reactive power flow along the branch is preferred to be zero (i.e. Qij = 0). Nevertheless, to maintain the voltage variation between buses i and j at a minimum, the reactive power flow is preferred to be equal to −(rij /xij ) · Pij . In [18], it is suggested that a control scheme should be adaptable to easily allow for smooth transitions between emphases on power quality and distribution losses. The minimizations of loss and penalty objective functions formulated in (6) and (7), respectively, are compared in Section 5. Loss minimization demonstrates the economical aspect while voltage deviation in the objective represents the technical limitations. The utilization of DG reactive power and impact of real-time thermal rating for CVC is the focal point of this study. Ultimately, however, advanced centralized optimal coordinated voltage controls are expected to be multi-objective, encompassing the following: • Maintain voltage within permitted range and flatten voltage profile along feeders • Minimize the sum of: o Energy losses o Curtailed DG energy o Operation (wear) of network components (OLTC, VR, SC etc.) o Reactive power flow through HV/MV transformer o Reactive power injection/absorption by DG

4.1.1. Loss minimization objective The loss minimization objective is formulated in the following equation:

Min PL =

N N

i=1



gi,j Vi 2 + Vj 2 − 2Vi Vj cos ıi − ıj



(6)

j=1

  V  G N

−PDGi + PDi + Vi

ij cos

j





+ Bij sin ij

ij

(8)

= 0 i = 1, . . ., N

j=1

  V  G N

−QCi − QDGi + QDi + Vi

j

ij sin

 ij



− Bij cos ij

= 0 i = 1, . . ., N

j=1

(9)

⎧ Vi V  PDGi · tan (acos (PFlim )) , ⎪ ⎪ i ⎪ ⎪ ⎪ ⎪ ⎪ 1 0, ⎨ − D ≤ Vi ≤ 1 + D QDGi =

P

· tan (a cos (PF

Vi < 0.9 or Vi > 1.1

))

lim DGi (−Vi + 1 + D) , 1 + D < Vi ≤ 1.1 ⎪ ⎪ 0.1 − D ⎪ ⎪ ⎪  ⎪ ⎪ ⎩ PDGi · tan (acos (PFlim )) −Vi + 1 − D , 0.9 ≤ Vi < 1 − D

(10)

0.1 − D

where  ij = ıi − ıj is the voltage angle difference between connected buses i and j. QDGi is the reactive power supplied or absorbed by the DG connected to bus i. (8) and (9) calculate active and reactive power injections at bus i, respectively. The network admittance matrix is given by Yij = Gij + i × Bij . (10) sets the DG reactive power supply following the Q/V droop characteristics,

Vimin ≤ Vi ≤ Vimax ,

i = 1, . . ., N,

QDGi min ≤ QDGi ≤ QDGi max , QCi min ≤ QCi ≤ QCi max ,

where N is the total number of buses and gk (gi,j ) is the conductance of branch k or the line connecting node i to j. Vi and Vj are the voltage magnitudes and ıi and ıj are voltage angles for nodes i and j, respectively.

4.1.2. Voltage penalty function objective In addition to the loss minimization objective defined in (6), a penalty function for the voltage exceeding a certain threshold can be defined as in the following equation:

⎧ k(V − Vi )2 ; Vi < Vimin ⎪ ⎨ imin ⎪ ⎩

4.2. The equality constraints

4.3. Inequality constraint



/ i j=

Wi =

Fig. 6. Voltage penalty function.

0;

Vimin ≤ Vi ≤ Vimax

k(Vi − Vimax )2 ;

Vi > Vimax

(7)

where k is the penalty factor. The objective function in (7), also drawn in Fig. 6, can be used when the voltage quality is more significant than the overall distribution network losses.

akmini ≤ aki ≤ akmaxi

  Sij  ≤ Sij,max

0 ≤ PDGi ≤ PDG

∀i ∈ NDGq

(11) (12)

∀i ∈ NCq

(13)

∀i ∈ NOLTC

(14) (15)

gen,i ,

i = 1, . . ., N,

(16)

where (11) limits the upper and lower voltage magnitude at bus i, (12) sets the limits for DG reactive power at bus i, (13) limits the reactive power supply from the SVCs, (14) gives the range of OLTC set-points and (15) gives the real-time dynamic thermal rating or static rating of branch ij. Eq. (16) prevents the utilized DG generated power PDGi at node i from exceeding the actual DG generated power PDG gen,I , NDGq , NCq , and NOLTC are the set of all DG units, SVCs and OLTCs connected at bus i, respectively. Sij,max is the capacity of the line or cable which is calculated using the dynamic thermal models of the overhead lines and underground cables. The previous hour’s optimal loading of the branch is used to attain the initial conductor temperature for calculating the coming hour’s line or cable rating. Hence, the iteration between the OPF with CVC and the DTR is established. In the optimization problem defined by (6)–(16), the control variables are the reactive power of the DG units (QDGi ), the reactive power of the SVCs (QCi )

46

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

Fig. 7. Greenfield network plan based on actual loading data and geographical location [21]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

and the tap set-point (ak ). The state variables, on the other hand, are the bus voltage magnitude and angle, while the line load flows are output variables. Due to the nonlinearity of power systems, linear programing loses accuracy due to linear assumptions [19]. Hence, the OPF is solved using the nonlinear IPOPT solver of the General Algebraic Modeling System (GAMS), while the DTR has been implemented in MATLAB [20]. For numerical efficiency within the power flow or the OPF solution all discrete variables (transformer taps and shunt steps) are treated as continuous until the optimal solution is found. Then they are rounded off to their nearest discrete values. The day-ahead dynamic thermal ratings of the distribution network components in Fig. 5 are attained from the load and weather variable forecasts’ input into the dynamic thermal models of the components. The day-ahead dynamic thermal rating procedure is presented in [17].

5. Test case: An active distribution network with DG units and voltage regulating devices For the test case, a Greenfield distribution network plan based on actual loading data and geographical location is used, as shown in Fig. 7. In the single line network diagram the green lines represent MV underground cables while the red lines are overhead. The test distribution network has 146 20/0.4 kV secondary substations and a 110/20 kV primary substation. The distribution network has voltage regulating devices, an OLTC at primary substation and two SVCs installed at the load center of the network. Besides, wind turbines are installed at four locations and solar panels are installed at three locations, as shown in Table A.1. In this work, various formulations of the CVC problem for day-ahead distribution network operation are investigated. The most important alternative solutions studied are the involvement of DG units in supplying or absorbing reactive power through the

CVC scheme and the implementation of a real-time thermal rating system. In the test network, the secondary substation one day loading is selected randomly from a pool of hourly AMR meter measurements from actual households. The random selection considers the data pool to be uniformly distributed. The respective reactive power loads are calculated to correspond to the residential loading power factor range of 0.955 to 0.98. Although the forecasts of the day ahead load and weather variables are used to compute the optimal CVC set-points for day ahead network operation, the forecasting method is not elaborated in this study. The day ahead dynamic thermal ratings and weather and load forecasting methods employed in this study are presented in publications [16,17]. By definition, the DG penetration level in a system is the ratio of gross annual energy generated by the DG to the total annual energy demand in the system. In this study DG penetration levels of 1.13%, 11.3%, 22.6% and 65% are investigated. The DG capacity presented in Table A.1 is at 1.13% penetration level, which is also the first case scenario. Mainly the scenarios for ten and twenty-fold increases in the DG penetration levels are investigated, which are 11.3% and 22.6%, respectively. To represent a high DG penetration we also simulated a 65% penetration level. The installed DG units, however, are not evenly distributed throughout the network; rather, only the installed capacities are varied at their respective fixed geographical locations, as shown in Fig. 7. There are around 30 radial feeders connected to the primary substation, of which the longest line is 60 km. Details of the test distribution network are provided in Tables A.1 and A.2. In Fig. 8, the bus voltages of the feeder starting from the primary substation are plotted for a network without DG units and a network with 65% penetration of DG units. There is no CVC applied in the case shown in Fig. 8 and the voltage levels are the average of the 24 h voltage levels. The test distribution network without DG integration (see Fig. 8a) has 2.4% higher losses on the selected day than the DG integrated test network (see Fig. 8b) with a 65% DG penetration level. In Fig. 9, the substation voltage level on the 30 feeders of the test

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

47

1.001

Voltage level (pu)

1

0.999

0.998

0.997

(a)

0.996 0

10

20 30 40 Distance from primary substation (km)

50

60

1.15

Voltage level (pu)

1.1

(b)

1.05

1

0.95 0

10

20

30

40

50

60

Distance from primary substation (km) Fig. 8. Daily average voltage levels of buses on the 30 feeders radiating from the primary substation for the test distribution network without DG (a) and with 65% DG penetration (b) (in (b) the blue feeders are connected with wind turbines and the red feeders are connected with solar panels). In both (a) and (b), there is no CVC applied. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

network is plotted before and after the CVC is applied. Fig. 9a shows the case for a 65% DG penetration level while Fig. 9b shows the case for 1.11% DG penetration. The CVC corrects both the overvoltages caused by DG connected at the end of radial feeder and undervoltages due to long distances from the primary substation. From Fig. 9 it is also apparent that the two-third rule for SVC placement on a radial feeder does not apply in the test network, where the DG units are scattered at the ends of the feeders. In this study, the day ahead model predictive CVC strategy is applied on the test distribution network by varying the CVC objective functions and the network rating types. The results in Table 1 compare the six types of CVC formulation involving DG units at 1.13% penetration level with DG curtailment, and at 11.3% and 22.6% penetration level, with and without DG curtailment. Table 1 presents the overall network losses after applying the control setpoints for a period of 24 h. Besides, the number of OLTC and SVC operations per day, and the cumulative reactive power supplied by DG units and SVCs are presented. The lowest network losses are attained, as expected, for a CVC formulation where loss minimization is the objective. Apparently there is no difference between static and dynamic rating when loss minimization is the only objective as DTR does not directly reduce losses. Nevertheless, the DG soft curtailment is too high when voltage loss minimization is the objective. DTR shows a clear advantage over static rating in terms of maximizing the utilization of the DG units, while SVCs are effective for voltage control and reducing the stress on OLTCs. However,

the greater utilization of active power generation from the DG units came with a slight increment in losses. A voltage penalty function can minimize the voltage burden on the customer. As shown in Fig. 10, the static and DTR ratings coupled with both the voltage penalty function and loss minimization gave the voltage level closest to the nominal. DTR, therefore, enables the proper utilization of resources for CVC, where a superior benefit can be attained by using DTR coupled with the penalty function and loss minimization objectives. The following characteristics of the CVC objective function formulation methods are observed: Observation no. 1: The CVC formulations experienced a higher voltage level from the nominal without the involvement of DG reactive power capacity than with (see Fig. 11). In addition, the optimal set-point is achieved at significantly higher network loss values for CVC without DG reactive power involvement. Observation no. 2: With the voltage deviation penalty function objective; there is a higher requirement for the operation of the SVCs and OLTCs, as shown in Table 1. In both Static and DTR rating methods, the voltage penalty function objective utilizes a higher reactive power supply from the SVCs and OLTCs while injecting reactive power into the DG units. This is because the objective places less emphasis on losses, leading to a greater tendency to use reactive power absorption and supply to keep the voltage level in the entire network close to unity. With the voltage penalty function objective, the voltage level stays closer to the flat one per

48

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

1.16

65% DG penetration without CVC 65% DG penetration with CVC+DTR+LOSS+PENALITY

1.14

Voltage level (pu)

1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 0

(a)

10

20 30 40 Distance from primary substation (km)

50

60

1.0005 1.13% DG penetration without CVC 1.13% DG penetration with CVC + DTR + Loss

Voltage level (pu)

1

0.9995

0.999

(b)

0.9985 0

10

20 30 40 Distance from primary substation

50

60

Fig. 9. An average day-ahead voltage level profile of the secondary substations on the 30 feeders, with and without the implementation of CVC. (a) shows the profile with 65% of DG penetration and (b) shows the result with a 1.13% DG penetration level.

unit compared to the loss minimization objective function. However, the network losses increased tremendously with the voltage penalty function objective, as shown in Table 1. With the penalty function objective, DTR can use the reactive power resources and 1.0015 No CVC CVC+STATIC+Loss CVC+STATIC+Penality CVC+DTR+Loss CVC+DTR+Penality CVC+STATIC+Loss+Penality CVC+DTR+Loss+Penality

1.15 No CVC STATIC loss minimization CVC without DG STATIC loss minimization CVC with DG

1.0005

Voltage level (pu)

Bus voltage magnitude (pu)

1.001

also lower the DG active power generation curtailment better than static ratings, as shown in Table 1. Observation no. 3: DTR shows no significant difference from static rating when loss minimization is an objective. In principle, the DTR utilizes the opportunities provided by the weather for the cooling of distribution network components. It is evident that with

1

1.1

1.05

0.9995

1 0.999 0

5

10

15 20 25 Distance from primary substation (km)

30

35

Fig. 10. Voltage level at hour 4:00 on feeder 10, where a wind turbine is connected at the furthest node. The DG penetration level is 1.13% and the CVC involves DG curtailment.

0

10

20

30

40

50

60

Distance from primary substation (km)

Fig. 11. Voltage level on the longest feeder of the network after implementation of CVC with and without the involvement of DG reactive power supply. (In all the three scenarios, 65% DG penetration.)

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

49

Table 1 Evaluation of the CVC formulation techniques for the period of 24 h ahead implementation. No.

Specification (objective and rating)

DG penetration (%)

DG curtailment

Losses (kW h)

Max. Vdev* (%)

1

Obj: losses & rating: static

1.13 1.13 11.3 11.3 22.6 22.6

Yes No Yes No Yes No

25.6 34.5 23.0 2,610.7 22.8 10,352.5

0.14 0.14 0.14 0.91 0.14 1.83

2

Obj: losses & rating: DTR

1.13 1.13 11.3 11.3 22.6 22.6

Yes No Yes No Yes No

25.6 34.5 23.0 2,609.6 22.831 10,352.5

3

Obj: penalty & rating: static

1.13 1.13 11.3 11.3 22.6 22.6

Yes No Yes No Yes No

4

Obj: penalty & rating: DTR

1.13 1.13 11.3 11.3 22.6 22.6

5

Obj: losses + penalty & rating: static

6

Obj: losses + penalty & rating: DTR

*

Vdev = max(|1 − Vij |),

i = 1; 24,

No. of SVC operations

DG Qgen. (MVARh)

DG Pgen curtailed (%)

SVC Qgen. (MVARh)

0 0 0 0 0 0

0 0 0 12 0 27

2.439 1.016 1.459 −36.455 1.457 −73.620

31.63 0 90.39 0 94.97 0

0.856 0.994 0.946 7.521 0.946 15.146

0.14 0.14 0.14 0.89 0.14 1.83

0 0 0 0 0 0

0 0 0 10 0 25

2.438 1.017 1.459 −36.161 1.454 −73.620

31.64 0 90.39 0 94.97 0.00

0.858 0.991 0.947 6.584 0.954 15.147

47.9 55.8 2,981.9 3,261.6 10,798.6 11,502.7

0.24 0.28 3.56 3.56 1.86 3.88

11 9 10 16 16 17

1 2 20 31 31 32

−1.506 −2.185 −48.952 −50.713 −87.857 −92.136

2.27 0 0.69 0 0.12 0

9.866 11.915 50.989 56.733 63.214 78.740

Yes No Yes No Yes No

49.8 57.0 2,926.5 3,041.3 10,866.95 11,546.9

0.21 0.29 1.94 2.54 1.92 3.99

5 13 13 12 7 16

0 0 19 27 22 36

−1.647 −2.296 −49.411 −48.449 −89.359 −94.552

2.10 0 1.39 0 0.14 0

10.292 12.351 53.125 48.768 68.587 87.551

1.13 1.13 11.3 11.3 22.6 22.6

Yes No Yes No Yes No

36.0 34.5 2,544.5 2,613.9 10,302.71 10,352.5

0.16 0.14 0.89 0.91 1.83 1.83

6 0 5 2 4 0

2 0 0 3 4 3

0.929 1.021 −36.076 −36.641 −73.316 −73.619

4.23 0 0.97 0 0.31 0

1.867 0.979 6.775 8.051 14.752 15.143

1.13 1.13 11.3 11.3 22.6 22.6

Yes No Yes No Yes No

34.6 34.5 2,542.9 2,610.1 10,338.9 10,352.5

0.14 0.14 0.89 0.90 1.83 1.83

8 0 4 2 4 0

0 0 0 1 3 3

1.026 1.018 −36.113 −36.352 −73.553 −73.619

3.77 0 0.82 0 0.14 0

1.454 0.990 6.752 7.213 15.142 15.144

j = 1; 147.

DTR network losses could even increase as long as they remain within the economically acceptable level. As shown in Fig. 12 and Table 1, the voltage penalty minimization objective provides better voltage levels with DTR than with static rating, even though the total losses are the same.

1.035 1.03

DTR voltage penalty minimization STATIC voltage penalty minimization

1.025 Voltage leve (pu)

No. of OLTC operations

1.02 1.015 1.01 1.005

Observation no. 4: The combined loss minimization and voltage penalty objective function with both static and DTR rating reduced significantly the operations of OLTCs and SVCs, while utilizing both the active and reactive power resources of the installed DG units to the utmost. This has been observed in all the four cases presented in Table 1. The simulation results for the network loss minimization objective and the voltage penalty function objective in the CVC formulations are presented in Table 1. When network losses are insignificant, such as in the test network in Fig. 7, the voltage penalty function objective performs better, by bringing the voltage to a flat stable level close to one per unit. In addition, the incorporation of static rating or DTR with a loss minimization objective brought down the network losses by about 29%, compared to the static or DTR rating with only the voltage penalty function objective. Furthermore, when the voltage penalty function and loss minimization objectives are used together the observed overall performance is superior.

1

6. Discussion on practical implementations 0.995 0

20

40 60 80 100 The 147 buses in order of their number

120

140 150

Fig. 12. The voltage level at hour 16:00, after the static and DTR based CVC control settings are applied with the voltage penalty minimization objective and with 20% DG penetration.

Planning CVC for day-ahead distribution network operation requires reliable load and environmental variable forecasting. Nevertheless, the control setting planned a-day-before faces two fundamental challenges. The first is the question of where to

50

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

the benefits, primarily by reducing DG curtailment as observed in [13]. 7. Conclusion

Fig. 13. Integrated local and central voltage control strategy.

conduct the central optimization for CVC and how to communicate the optimal set-points to the respective equipment such as OLTCs, SVCs and DG units. The second challenge is how to react to contingencies during the same day and the requirements for updating. Usually, voltage regulators operate by following the voltage level at their connection point. In a CVC strategy, however, the optimal set-points are computed and communicated from elsewhere. We propose a connection point voltage dependent on central and local control strategies for the specific voltage regulators, as shown in Fig. 13. The day ahead optimal set-points will be sent to the specific voltage regulating device that it follows, unless the connection point voltage level does not violate a certain threshold. When the connection point voltage level violates a given preset level, however, the local closed loop control system will be initiated (see Fig. 13). This strategy can be implemented naturally with the Multi-Agent System (MAS) control architecture of active distribution networks. With the specified MAS approach, the voltage regulating devices need to be agents with decision making and communication capability. Another challenge in executing the optimal control settings is the proper queuing of the control actions. Hence, not only do we need to communicate the day-ahead control settings, but the associated time lags are also needed. The proposed method is mainly for active distribution network operations planning which might range from minutes ahead to up to a day-ahead. For real-time application, as is discussed briefly in this section, we propose a cooperative central and distributed control strategy. In the proposed scheme, the dayahead centralized operation planning (which can be referred to as coordinated control agents) will be used as a guideline for local controls (unit control agents). We believe that, to accommodate the distributed potentials such as DG units and demand response, a relaxed centralized cooperation strategy with decentralized control functions will be most useful. Such a multi-agent based hierarchical hybrid control architecture is presented in [22]. In future work, the addition of network reconfiguration capabilities in the proposed comprehensive CVC method would enhance

In this study, the synergy between coordinated voltage control and real-time dynamic thermal rating is investigated for an increased utilization of DG reactive power potential. Beyond its foremost benefits, enhancing network capacity and efficient utilization of network components, dynamic thermal rating has demonstrated its advantage for a coordinated voltage regulation involving DG units. The benefit of incorporating DTR with CVC is two-pronged. On one hand, the generated DG active power can be utilized better, due to an increased distribution network component carrying capacity. On the other hand, the required reactive power for voltage regulation can be transferred without violating network component limits if DTR is applied in a realtime basis. In the analysis, the CVC formulation with a combined loss and voltage penalty function objective and real-time dynamic thermal rating method showed better results in both minimizing the network losses and keeping the voltage close to one per unit. The day-ahead CVC network operation planning framework is not tested with very large networks, where computation times could better be investigated. The complete intended application, involving the interaction between day-ahead network operation planning and intraday local network operation control actions, has not yet been simulated. With the improved measurement points in today’s active distribution network, there has never been such a high degree of visibility and forecasting potential for distribution network component states and customer loads. Hence, multi-objective predictive control strategies could utilize DG for voltage regulation, and employ real-time thermal rating to increase the integration potential of new DG and to utilize available reactive power resources. Acknowledgements The authors of this paper would like to acknowledge that this work is jointly funded by the Aalto energy efficiency program through the SAGA and STEEM projects, and would also like to thank Jussi Niskanen of Loiste Sähkoverkko for his cooperation. Appendix A. Tables A.1 and A.2.

Table A.1 DG, SVC and OLTC connections.

DG

Type

Node

DG rating and number

WIND

102 108 92 66 28 83 117

50 kW × 2 Turbines 50 kW × 3 Turbines 50 kW × 2 Turbines 50 kW × 3 Turbines 215 Wp × 8 Panels 215 Wp × 32 Panels 215 Wp × 16 Panels

Max (MVA) 15 30 Max tap 1.11

Min (MVA) 0 0 Min tap 0.91

PV

SVC (0.5/opp.)

OLTC (0.0125/opp.)

Node 85 121 Place Primary substation

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

51

Table A.2 The 147 bus active distribution test network specifications (40 MVA base 20 kV MV system). No. 1u 2u 3u 4u 5u 6u 7u 8u 9u 10u 11u 12u 13u 14u 15u 16 17u 18u 19u 20u 21u 22u 23u 24u 25u 26 27u 28u 29u 30u 31u 32 33u 34u 35u 36 37u 38u 39u 40u 41 42 43u 44 45u 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64u 65 66 67 68 69u 70 71 72 73 u

From 16 32 20 13 1 38 2 41 2 1 30 14 1 3 22 33 28 21 29 1 1 4 8 10 35 37 9 12 6 1 7 18 30 40 41 17 1 5 23 31 24 49 19 78 72 82 72 84 68 63 43 52 58 62 55 52 71 54 61 59 61 50 45 51 65 43 96 84 44 98 109 74 88

To

r (pu)

x (pu)

No.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

0.008 0.005 0.010 0.005 0.003 0.004 0.013 0.019 0.006 0.053 0.006 0.006 0.007 0.005 0.010 0.021 0.014 0.005 0.005 0.017 0.018 0.017 0.027 0.006 0.004 0.022 0.013 0.005 0.003 0.022 0.004 0.033 0.002 0.007 0.005 0.011 0.002 0.006 0.005 0.024 0.035 0.035 0.018 0.018 0.011 0.013 0.032 0.035 0.046 0.113 0.027 0.066 0.027 0.047 0.098 0.018 0.024 0.026 0.071 0.074 0.050 0.088 0.020 0.011 0.013 0.019 0.032 0.049 0.018 0.048 0.029 0.021 0.138

0.006 0.004 0.008 0.004 0.003 0.003 0.010 0.015 0.005 0.042 0.005 0.005 0.006 0.004 0.008 0.026 0.011 0.004 0.004 0.014 0.014 0.014 0.021 0.005 0.003 0.027 0.010 0.004 0.002 0.018 0.003 0.040 0.002 0.006 0.004 0.013 0.002 0.005 0.004 0.019 0.043 0.043 0.015 0.023 0.008 0.017 0.039 0.043 0.057 0.139 0.033 0.082 0.033 0.058 0.121 0.023 0.030 0.032 0.087 0.091 0.061 0.109 0.025 0.008 0.016 0.023 0.040 0.061 0.014 0.060 0.035 0.026 0.170

74 75 76 77 78 79 80 81 82 83 84 85 86 87 88u 89 90 91 92 93u 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112u 113 114 115 116 117 118 119 120 121 122 123 124u 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

Branches of underground cables. All others are overhead lines.

From

To

r (pu)

x (pu)

77 97 48 81 78 86 80 46 79 76 47 94 79 89 90 27 90 55 49 70 74 69 48 73 134 99 100 101 113 103 104 107 108 56 64 111 125 110 100 104 123 126 110 116 128 135 140 138 122 115 11 119 112 146 143 142 130 127 141 133 129 137 127 139 140 136 124 129 145 124 119 147 42

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

0.037 0.017 0.019 0.042 0.037 0.021 0.020 0.036 0.027 0.043 0.028 0.032 0.037 0.024 0.020 0.285 0.036 0.082 0.053 0.020 0.047 0.029 0.027 0.050 0.130 0.026 0.058 0.051 0.047 0.029 0.066 0.064 0.104 0.256 0.022 0.077 0.032 0.019 0.023 0.086 0.024 0.040 0.028 0.028 0.028 0.032 0.028 0.027 0.041 0.055 0.040 0.015 0.062 0.029 0.019 0.060 0.016 0.031 0.072 0.021 0.097 0.055 0.068 0.072 0.026 0.039 0.032 0.046 0.027 0.048 0.021 0.042 0.133

0.046 0.021 0.023 0.052 0.046 0.026 0.025 0.044 0.034 0.053 0.035 0.039 0.046 0.029 0.016 0.351 0.044 0.102 0.065 0.016 0.058 0.036 0.033 0.062 0.161 0.032 0.071 0.063 0.058 0.036 0.082 0.078 0.128 0.315 0.028 0.095 0.039 0.023 0.018 0.105 0.029 0.050 0.035 0.035 0.035 0.039 0.035 0.034 0.051 0.068 0.032 0.018 0.076 0.035 0.023 0.074 0.020 0.039 0.089 0.026 0.120 0.068 0.084 0.089 0.032 0.048 0.039 0.056 0.033 0.059 0.026 0.051 0.165

52

M.Z. Degefa et al. / Electric Power Systems Research 127 (2015) 41–52

References [1] M.E. Elkhatib, R. El-Shatshat, M.M.A. Salama, Novel coordinated voltage control for smart distribution networks with DG, IEEE Trans. Smart Grid 2 (Dec (4)) (2011) 598–605. [2] A. Samadi, R. Eriksson, L. Soder, B.G. Rawn, J.C. Boemer, Coordinated active power-dependent voltage regulation in distribution grids with PV systems, IEEE Trans. Power Delivery 29 (June (3)) (2014) 1454–1464. [3] S. Engelhardt, I. Erlich, C. Feltes, J. Kretschmann, F. Shewarega, Reactive power capability of wind turbines based on doubly fed induction generators, IEEE Trans. Energy Convers. 26 (March (1)) (2011) 364–372. [4] A. Kulmala, S. Repo, P. Järventausta, Using statistical distribution network planning for voltage control method selection, in: IET Conf. Proc. on Renewable Power Generation, Sept 2011, Edinburgh, UK, 2011. [5] N. Daratha, B. Das, J. Sharma, Coordination between OLTC and SVC for voltage regulation in unbalanced distribution system distributed generation, IEEE Trans. Power Syst. 29 (1) (2014) 289–299. [6] D. Ranamuka, A.P. Agalgaonkar, K.M. Muttaqi, Online voltage control in distribution systems with multiple voltage regulating devices, IEEE Trans. Sustainable Energy 5 (Apr (2)) (2014) 617–628. [7] A. Viehweider, B. Bletterie, D.B. De Castro, Advanced coordinated voltage control strategies for active distribution network operation, in: CIRED 20th Int. Conf. on Electricity Distribution, 8–11 Jun, 2009, Prague, 2009. [8] A. Kulmala, K. Maki, S. Repo, P. Jarventausta, Including active voltage level management in planning of distribution networks with distributed generation, in: Proc. IEEE PowerTech, Jun. 2009, Bucharest, 2009, pp. 1–6. [9] F.A. Viawan, D. Karlsson, Voltage and reactive power control in systems with synchronous machine-based distributed generation, IEEE Trans. Power Delivery 23 (Apr (2)) (2008) 1079–1087. [10] P.M. Carvalho, P.F. Correia, L.A. Ferreira, Distributed reactive power generation control for voltage rise mitigation in distribution networks, IEEE Trans. Power Syst. 23 (May (2)) (2008) 766–772.

[11] F. Capitanescu, I. Bilibin, E. Romero Ramos, A comprehensive centralized approach for voltage constraints management in active distribution grid, IEEE Trans. Power Syst. 29 (Nov (2)) (2013) 933–942. [12] T. Sansawatt, L.F. Ochoa, G.P. Harrison, Smart decentralized control of DG for voltage and thermal constraint management, IEEE Trans. Power Syst. 27 (Mar (3)) (2012) 1637–1645. [13] I. Bilibin, F. Capitanescu, Contributions to thermal constraints management in radial active distribution systems, Electr. Power Syst. Res. 111 (Jun) (2014) 169–176. [14] T.J.T. Hashim, A. Mohamed, H. Shareef, A review on voltage control methods for active distribution networks, Prz. Elektrotech. 88 (Jun) (2012) 304–312. [15] M. Vandenbergh, V. Helmbrecht, D. Craciun, R. Hermes, H. Loew, Technical solutions supporting the large scale integration of photovoltaic systems in the future distribution grids, in: CIRED 22nd Int. Conf. on Electricity Distribution, Jun 2013, Stockholm, 2013. [16] M.Z. Degefa, M. Humayun, A. Safdarian, M. Koivisto, R.J. Millar, M. Lehtonen, Unlocking distribution network capacity through real-time thermal rating for high penetration of DGs, Electr. Power Syst. Res. 117C (2014) 36–46. [17] M.Z. Degefa, M. Koivisto, R.J. Millar, M. Lehtonen, Dynamic thermal state forecasting of distribution network components, in: 13th Int. Conf. on Probabilistic Methods Applied to Power Systems (PMAPS 2014), 7–10 Jul., 2014, Durham, 2014. [18] K. Turitsyn, S. Petr, B. Scott, C. Michael, Options for control of reactive power by distributed photovoltaic generators, Proc. IEEE 99 (6) (2011) 1063–1073. [19] W. Zhang, F. Li, L.M. Tolbert, Review of reactive power planning: objectives, constraints, and algorithms, IEEE Trans. Power Syst. 22 (Nov (4)) (2007) 2177–2186. [20] E.R. Sichard, GAMS: A User’s Guide, Tutorial, GAMS Development Corporation, Washington, Mar. 2014. [21] R.J. Millar, S. Kazemi, M. Lehtonen, E. Saarijärvi, Impact of MV connected microgrids on MV distribution planning, IEEE Trans. Smart Grid 3 (4) (2012) 2100–2108. [22] C.X. Dou, B. Liu, Multi-agent based hierarchical hybrid control for smart microgrid, IEEE Trans. Smart Grid 4 (Jun (2)) (2013) 771–778.