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1 Edinburgh Research Exporer Network distributed generation capacity anaysis using OPF with votage step constraints Citation for pubished version: Dent, CJ, Ochoa, LF & Harrison, G 2010, 'Network distributed generation capacity anaysis using OPF with votage step constraints' IEEE Transactions on Power Systems, vo 25/1, pp DOI: /TPWRS Digita Object Identifier (DOI): /TPWRS Link: Link to pubication record in Edinburgh Research Exporer Document Version: Accepted author manuscript Pubished In: IEEE Transactions on Power Systems Pubisher Rights Statement: 2010 IEEE. Persona use of this materia is permitted. Permission from IEEE must be obtained for a other uses, in any current or future media, incuding reprinting/repubishing this materia for advertising or promotiona purposes, creating new coective works, for resae or redistribution to servers or ists, or reuse of any copyrighted component of this work in other works. Genera rights Copyright for the pubications made accessibe via the Edinburgh Research Exporer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these pubications that users recognise and abide by the ega requirements associated with these rights. Take down poicy The University of Edinburgh has made every reasonabe effort to ensure that Edinburgh Research Exporer content compies with UK egisation. If you beieve that the pubic dispay of this fie breaches copyright pease contact openaccess@ed.ac.uk providing detais, and we wi remove access to the work immediatey and investigate your caim. Downoad date: 04. Feb. 2018

2 1 Network distributed generation capacity anaysis using OPF with votage step constraints C.J. Dent, Member, IEEE, L.F. Ochoa, Member, IEEE, and G.P. Harrison, Member, IEEE Abstract The capacity of distributed generation (DG) connected in distribution networks is increasing, argey as part of the drive to connect renewabe energy sources. The votage step change that occurs on the sudden disconnection of a distributed generator is one of the areas of concern for distribution network operators in determining whether DG can be connected, athough there are differences in utiity practice in appying imits. To expore how votage step imits infuence the amount of DG that can be connected within a distribution network, votage step constraints have been incorporated within an estabished optima power fow (OPF) based method for determining the capacity of the network to accommodate DG. The anaysis shows that strict votage step constraints have a more significant impact on abiity of the network to accommodate DG than pacing the same bound on votage rise. Further, it demonstrates that progressivey wider step change imits deiver a significant benefit in enabing greater amounts of DG to connect. Index Terms Optimization methods, Load fow anaysis, Power generation panning. I. INTRODUCTION WORLDWIDE environmenta concerns have paced restrictions on new arge scae conventiona power station deveopments. Additionay, concerns over security of fue suppy have ed governments around the word to set targets to diversify their energy mixes in the forthcoming decades; indeed, incentives are aready in pace to encourage renewabe and combined heat and power deveopments. It is expected that a number of these deveopments wi be connected to the (traditionay passive) distribution network. Votage contro, faut eves, reiabiity and power osses are among the issues faced in integrating Distributed Generation (DG) which have been addressed in the iterature [1] [6]. Indeed, DG fundamentay changes the nature of distribution networks [7], [8], and therefore a number of studies have buit DG panning modes which consider the various technica requirements. In [9] [11], the DG siting and sizing probem was soved using impact indexes, whereas anaytica approaches were deveoped in [12], [13]. Mathematica optimisation approaches using metaheuristics [14] [16] and a inear programming formuation [17], have aso been appied. To take into account directy the intrinsic non-inearities of the probem, approaches based on AC optima power fow (OPF) modes have been proposed in [18] [21]. This work is funded through the EPSRC Supergen V, UK Energy Infrastructure (AMPerES) grant in coaboration with UK eectricity network operators working under Ofgem s Innovation Funding Incentive scheme fu detais on The authors are with the Schoo of Engineering, The University of Edinburgh, Mayfied Road, Edinburgh EH9 3JL, UK (Emai: chris.dent@ed.ac.uk, uis ochoa@ieee.org, Gareth.Harrison@ed.ac.uk). With higher penetration eves of DG, the benefits from appropriate siting of DG, whether driven by centra panning or a system of financia incentives, are increasing. In order to maximise the potentia of a network to accommodate DG, carefu panning is required as connection of generation at some ocations might significanty reduce the tota capacity for DG [19], [22], and hence imit export to the transmission system. This is a particuar concern where connection appications are deat with on a first-come, first-served basis, without an anaysis of the consequences for the network s tota capacity. When assessing network capacity for connection of generation, it is necessary to consider a significant technica and physica constraints. Most DG studies have, however, overooked a particuar requirement of the distribution networks: votage step constraints on oss of a generator, which is a quite distinct issue from votage rise. Votage step changes occur when a DG is started up or suddeny disconnected from the network, and imits are typicay paced on the maximum step change aowed. In particuar, in the UK, the Energy Networks Association s Engineering Recommendation (ER) P28 [23] specifies a imit of 3% for infrequent panned switching events or outages, and 6% for unpanned outages (e.g. fauts). There appears to be variation in UK practice regarding the aowabe magnitude and frequency of votage step changes (with some DNOs setting ess stringent design imits in weak parts of their networks [24]). Work by the Energy Networks Association is ongoing to estabish definitive practice. As a resut, it remains crucia to take votage step changes into account when evauating the accommodation of new DG [25], [26]. Whie the process of starting a generator may ead to step changes in votage eves, the sudden disconnection of a DG unit from the network due to fauts or other causes wi be the primary concern here. ER G75/1 [27] defines votage step change: Foowing system switching, a faut or a panned outage, the change from the initia votage eve to the resuting votage eve after a the Generating Unit automatic votage reguator (AVR) and static var compensator (SVC) actions, and transient decay (typicay 5 seconds after the faut cearance or system switching) have taken pace, but before any other automatic or manua tap-changing and switching actions have commenced. When using a power fow-based mode to assess votage step change, it can therefore be defined as the difference between the votage eve when the generation unit is connected, and the steady state votage eve with the same network topoogy

3 2 Fig. 1. GSP A R+jX B Two bus system for votage step anaysis. P DG +jq DG ~ P L +jq L but with the generator disconnected. Ceary, evauating the votage step change caused by disconnection of a singe DG unit is a straightforward procedure. Nonetheess, the compexity of the probem increases significanty when mutipe generators are considered in a panning probem, since a singe soution must satisfy the votage step constraint on oss of each generator. This paper proposes a optima power fow (OPF) method for assessing the DG capacity of network which for the first time incudes votage step imits on oss of a generator, in addition to the usua OPF constraints (e.g. votage eve, therma). This work buids on earier studies on generation capacity assessment by mathematica optimisation [19]. Votage step constraints are incorporated using a security constrained OPFike formuation, where the contingencies considered are outages of generators rather than branches. Whie a 3% imit has been used for most of the exampes in this paper, the methodoogy presented is generic, and woud appy at any incuding the wider 6% UK imit for unpanned outages, and the 5% imit in common use in the USA [28]. This paper is structured as foows: Section II introduces the votage step issue by way of a simpe two-bus mode. In Section III, the method for using an optima power fow (OPF) mode to determine network capacity for DG is described with the incusion of votage step constraints. Resuts from the method s appication to a rea part of the UK distribution network are presented and discussed in Sections IV and V. This demonstrates that a votage step imit can actuay be more restrictive of DG capacity than a votage eve imit with the same bounds. Finay, concusions are drawn in Section VI. A fu mathematica specification of the mode is given in Appendix A. II. VOLTAGE RISE AND VOLTAGE STEP Votage rise and votage step are reated but distinct phenomena. The differences between them may be iustrated using the two bus system shown in Fig. 1. This consists of a Grid Suppy Point (GSP) at bus A, and oad and generation at bus B. Where power is exported from the DG towards bus A, the steady state votage rise V BA between buses A and B is given approximatey by V BA = (P DG P L ) R + (Q DG Q L ) X, (1) where P DG and Q DG are the rea and reactive outputs of the generator. Subtracting the votage rise with the DG disconnected from the votage rise with the DG connected, the votage step V S at bus B on oss of the generator (assuming that the votage at A remains constant) is V S = (P DG R + Q DG X). (2) Unike votage rise, the step depends on the fu output of the generator, and is not mitigated by oad at the bus, or by transformer tap settings. As a consequence, for a given imit on percentage deviation, the votage step imit is expected to restrict DG capacity more than the commony considered votage eve imits. If the generator is operated at agging power factor, the reactive fow tends to reinforce the votage step (and rise) due to the the generator active power output. At eading power factor the reactive fow tends to reduce the votage step; conceivaby, shoud the generator consume enough reactive power the votage step may be upward. The robustness of this simpe two-bus mode for assessing quantitativey votage step changes wi be expored in Section V. Nevertheess, it wi be usefu in interpreting quaitativey the resuts presented ater. III. DG CAPACITY ANALYSIS USING OPF MODELS A. Previous Work A range of optimisation toos have been appied to probems in optima DG siting. In network generation capacity assessment (or, aternativey, capacity aocation) these range from the use of a fu AC optima power fow (OPF) mode [19], and inear programming modes incuding approximate impementations of faut, votage and therma constraints [22], to the use of genetic agorithms [29] (which aso considered investment and operationa costs, and osses, in a mutiobjective probem). Other approaches to DG optimisation probems at distribution eve have incuded tabu search for oss minimisation [30] and a genetic agorithm to decide the optima investment schedue over a number of years [15] (this aows the consideration of investment deferra benefits from DG.) The OPF for DG capacity anaysis is based on the concept that the network s capacity for new generation may be found by pacing DG expansion sites at the appropriate buses, and using an OPF mode to evauate the maximum tota generation which the network can support at these sites [19]. It requires ony sight modifications to the OPF mode used for cassica appications such as cost minimisation, which aready incudes Kirchhoff s aws, therma and votage constraints. The capacity at each site is a decision variabe in the probem, as opposed to a fixed parameter. As is common with DG [31], the generators are assumed to be run in constant power factor mode (i.e. with no votage contro), athough aternative operationa modes are possibe [32]. This method has aready been extended to incude faut eve constraints [33] and evauating the maximum capacity with a fixed number of DG sites [34]. The objective function is simpy the tota DG active power capacity in the network, i.e. the sum over the individua capacities p n of the new generators n: max n N p n. (3)

4 3 The simpest version of the OPF method may be impemented in some commercia power systems modeing packages [19]. However, more advanced features such as votage step and faut eve constraints necessitate a bespoke OPF formuation. A fu mode specification is given in Appendix A. B. Votage Step Constraints With votage step defined on the basis of conditions preand post-disconnection of the DG, it can be viewed as being anaagous to a ine outage contingency. Line outage security constraints have been incuded in OPF modes for many years; these modes are typicay referred to as Security Constrained OPFs (SCOPF, see [35] for a review of methods and appications). The generic formuation is to incude as constraints in the OPF a set of power fow equations in the revised network topoogy for each outage considered. This ensures that immediatey post-contingency a oad can sti be suppied with no votage and therma imit vioations. For the fu noninear AC OPF required for distribution networks, the entire power fow must be inserted into the mode to impement imits even on just one ine. Votage step constraints can be impemented simiary to the SCOPF where each contingency is an outage of a new DG site, and is therefore abeed by an index n. For each contingency network a set of power fow equations is added as constraints to the OPF mode. The contingency power fow equations are identica to the base case ones with the exceptions that the power injected from the outage generator is zero, and that contingency votage variabes, ine fows, etc. are used in the constraints where appropriate. The votage step constraint itsef takes the form V b V + S V n,b V b + V + S n N, (4) where for an outage of generator n, the contingency votage V n,b at bus b must differ from by no more than V + S from the pre-outage votage V b. C. Votage Reguation Transformer tap settings are used in distribution networks to keep the secondary bus votages as cose to target votage (typicay nomina) as possibe. Athough rea tap changers operate in discrete steps, in the OPF the tap ratios are treated as continuous decision variabes (modeing discrete settings woud resut in a much harder mixed integer noninear optimisation probem.) Foowing the practice in [19], a transformer secondary buses are constrained to exacty nomina votage in the intact network. The existence of parae transformers between the same bus or mutipe paths through the network means that highy unbaanced power fows on transformer pairs are possibe. In order to avoid this, mutipe transformers connected in parae to the same bus are constrained such that their tap settings are equa. This mirrors actua transformer practice, athough it is aso possibe to imit the difference in tap settings where mutipe paths are not exacty equivaent. To meet the definition of votage step change (Section I), the tap settings appied in the post-outage contingency power fows are identica to those in the pre-outage fows (i.e. the votage step is defined before the transformers have time to react to the oss of infeed). D. Redundancy Constraints Distribution networks are designed with buit-in redundancy in order to ensure continuity of suppy during outages [36]. Typicay the mutipe suppy paths to the oad woud take the form of parae transformers at substations, and doube circuits or reconfigurabe connections to neighbouring sections of the network. Where DG is expected to export significant amounts of power through parae sets of transformers and circuits, the worst-case firm connection assessment woud assume that one of the circuits is out-of-service. This wi typicay reduce the connectabe capacity at that site, and as a resut may infuence capacity esewhere. To ensure that the fow may be carried by one component aone during an outage, an approximate approach is to constrain the tota fow in parae pairs of components to the smaer of the components therma imits. Whie it does not treat exacty parae network sections whose ayouts are not exacty symmetrica, it barey increases the size of the mathematica optimisation probem. Further work is panned on this. E. Impementation The OPF is impemented in the AIMMS optimisation modeing environment [37], a high eve anguage in which the mode structure is defined in a manner amost identica to its paper formuation (given in Appendix A). In common with other optimisation modeing anguages [38], the mathematica program is generated by AIMMS from the mode structure and data with the first and second derivatives of the constraints evauated automaticay for non-inear modes. The mathematica program is sent to the CONOPT genera reduced gradient sover [37], which has proved absoutey reiabe in convergence on a cass of much arger security-constrained OPF probems [39], and is reasonaby efficient. A. Test Network IV. CASE STUDY The capacity evauation method is demonstrated on the sma section of the UK distribution network shown in Fig. 2, a subsection of the network presented in the origina paper to use OPF for DG capacity evauation [19]. The mainy rura network has significant potentia for wind and other renewabe deveopments, and is representative of many UK networks. Key network parameters are isted in Appendix B. For the initia anaysis, votage step constraints are ignored and potentia DG is aowed to connect at buses 21, 23 and 26. The secondary buses of transformers are reguated to nomina votage, with tap ratios constrained between 0.9 and 1.1, and the tap settings of parae transformers aowed to vary independenty. In the base case, steady-state bus votages at 11 and 33 kv are constrained within ±3% of nomina to satisfy the more onerous panning requirements of Engineering Recommendation P28 [23], rather than the ±6% aowabe by statute [40]. The GSP at bus 6 is at nomina votage.

5 4 132 kv TABLE I ACTIVE CONSTRAINTS WITHOUT VOLTAGE STEP CONSTRAINTS Power factor Active constraints 0.95 agging V + (b 22 ), V + (b 24 ), f + (t ) unity V + (b 25 ), f + ( ), f + (t ) 0.95 eading f + ( ), f + (t ), f + (t ) 33 kv 21 ~ 23 ~ 22 Fig. 2. Section of UK distribution network. Buses 21, 23 and 26 are at 11 kv. DG Capacity (MW) DG Capacity (MW) ~ Excuding step constraints 0.95 ag unity 0.95 ead Incuding step constraints Bus 26 Bus 23 Bus ag unity 0.95 ead Fig. 3. DG capacity without (top) and with (bottom) votage step constraints appied for three DG power factors. The maximum DG capacity (MW) avaiabe in the network is shown in Fig. 3 (top) for DG power factors fixed at 0.95 agging, unity and 0.95 eading. The resuts are consistent with those presented using the same network in [19]. The active inequaity constraints, i.e., those restricting DG capacity, are isted in Tabe I where V (+, ) (b) denotes the (upper,ower) votage imit at bus b and f + (, t) the therma imit on a ine or transformer. The capacity avaiabe at eading DG power factor exceeds that at agging power factor by around 21 MW. Operation at agging power factor resuts in a tendency for active and reactive power fows to be in the same direction, jointy contributing to votage rise. In this case upper votage imits TABLE II ACTIVE CONSTRAINTS WITH VOLTAGE STEP CONSTRAINTS ENFORCED Power factor Active constraints 0.95 agging f + (t ), V S (b 23, g 23 ), V S (b 26, g 26 ) unity f + (t ), V S (b 23, g 23 ), V S (b 25, g 26 ) 0.95 eading f + ( ), f + (t ), f + (t ) on the 33 kv feeders (at buses 22 and 24) constrains capacity at buses 23 and 26 to 31 MW and zero MW respectivey. At eading power factor, active and reactive fows are in opposite directions, reducing votage rise, with therma imits becoming binding. As the circuits from bus 6 to 20 have high capacity and reativey ow reactance, the generation at bus 21 is aways restricted to around 9 MW by the therma imit of the transformer connecting it to bus 20. B. Appying Votage Step Constraints If a imit of ±3% is paced on the votage step at each bus on oss of a generator, the DG capacity abe to be connected changes as shown in Fig. 3 (bottom), as do the active constraints (Tabe II). In addition to the symbos defined earier, V + S (b, g) and V S (b, g), respectivey denote the upper and ower votage step constraint at bus b when generator g disconnects. Upwards votage steps are taken as positive and vice versa. At eading power factor, the resut is identica to that without step constraints as, once more, active and reactive power contributions to the votage step party cance and the therma constraints become active before the votage step imits. The votage step constraints significanty reduce the tota generation capacity at agging and unity power factors (by 22 and 32 MW respectivey). Capacity at buses 23 and 26 is constrained by the aowed votage step at those buses or the primary bus of the associated transformer, when the votage steps are not mitigated by the DG reactive power export. The primary bus constraint is active at unity power factor, on disconnection of the DG at bus 26; the votage step of 3% at bus 25 is then sighty greater than that of 2.94% at bus 26. This unexpected resut occurs because the transformer connecting 25 and 26 is modeed as having reactance ony. With no reactive power fow from the DG the transformer impedance effectivey makes no contribution to the votage step. Capacity at bus 21 remains the same on imposition of votage step constraints; it is sti restricted by the therma constraint on its associated transformer. It is notabe that here the votage rises at generators are smaer than the votage steps on oss of the generators. As stated in Section II, this wi usuay be the case as votage rise is for a given network state determined by the actua

6 5 TABLE III OPTIMAL REAL POWER CAPACITIES AND POWER ANGLES. Generator Capacity (MW) Power factor Bus agging Bus eading Bus eading Tota power fows (i.e. generation minus oad) whereas votage steps are determined by the generator output without subtraction of demand. In addition, votage rise may be reduced using transformer settings, whereas this has a much smaer infuence over the step changes. C. Variabe Power Factor It is cear that the DG power factor pays a major roe in determining maximum capacity. As a resut, where fexibiity of power factor is aowed, capacity can be increased [32]. To investigate this further, the DG power factors (stricty the power anges) were treated as independent decision variabes in the OPF. Re-running the assessment with power factor aowed to vary between 0.95 eading and agging, the optima DG parameters are as shown in Tabe III; the tota capacity increases by 3MW over the 0.95 eading power factor case. With the increase in contro variabes, the number of active constraints restricting the optima soution increased from three to six: votage step at V + S (g 23, b 22 ) and V + S (g 26, b 25 ); therma constraints f + ( ), f + (t ) and f + (t ); and the ower tap imit on the bus 7 to 20 transformer. Independenty of the other generators, DG capacity at bus 21 is aways imited by the transformer therma constraint with the power factor chosen to maximise the rea power export. At the other two buses, the optima power factor is usuay determined by the votage step and rise imits. Resuts obtained with synchronisated tap settings for parae transformers have been compared with those where tap settings are aowed to vary independenty. For the variabe power factor case, the capacity under independent operation is negigibe, but the reactive fows between buses 6 and 20 become highy unbaanced (the synchronised case showed approximatey equa reactive fows.) When redundancy constraints are added (so that where parae branches exist one branch aone can support the entire power fow in case of an outage, see Section III-D) the network capacity reduces by 10.7 MW. The change occurs on bus 23 aone; the circuits connected to bus 20 have sufficienty high imits that the redundancy constraints do not affect the other generator sites. D. Dependence of Capacity on Votage Step Limit The variation of optima DG capacity with aowabe votage steps of up to 6% is shown in Fig. 4 for the fixed and variabe power factor cases. Fig. 5 shows the casses of active constraints which imit the capacity in the variabe power factor case. At fixed power factors of 0.95 agging and unity there is an approximatey inear reationship between connectibe Network DG capacity (MW) ag unity 0.95 ead variabe Maximum aowed votage step (%) Fig. 4. Variation of the optima DG capacity with maximum aowed votage step, both a range of fixed power factors and for variabe power factors. capacity and aowabe votage step with the maximum votage step acting as a significant constraint on capacity. At 0.95 eading power factor the capacity is very sensitive to votage step imit, athough when the imit exceeds 3% its effect is mitigated sufficienty that other constraints become active. Operation with variabe power factor again aows greater capacity to connect across a votage step imits, and is sighty ess sensitive to votage step imits than eading power factor operation. As might be expected, at sma votage step toerances, these constraints dominate, athough this coud be aeviated to some extent by aowing a wider range of power factors. The first quaitative change occurs when the step imit reaches 2%, at which point the ony two active step constraints are those at the primary buses of the transformers connected to buses 23 and 26, on oss of the generators at those buses. As the step constraint is reaxed further, the upper votage imit at bus 25 becomes active in pace of the step constraint on oss of the generator at 26. Finay, with the step imit above 5%, the aowed range of power anges does not aow sufficient reactive power generation to maintain the votage imit at 25 with the associated transformer at its therma imit, and some generation capacity transfers from bus 26 to bus 23. When a therma imit in one of the parae branches is active, the reevant redundancy constraint reduces the effective degrees of freedom of the system by one; this is why for votage step imits above 2% there are ony five active constraints. V. DISCUSSION This paper demonstrates a nove and effective means of incorporating votage step change constraints within assessment of distribution network capacity for connecting new DG. This is beieved to be the first work to demonstrate the importance of votage step change in the context of DG connection and panning. The step constraints are incuded within the OPF in a manner that mirrors that of the we known security constrained OPF by incuding contingency power fow equations in the optimisation mode. The enforcement of reativey

7 6 Active constraints Maximum aowed votage step (%) Pfactor Therma Veve Vstep Votage step (% of nomina) g, exact 0.95 g, approx Unity, exact Unity, approx 0.95 d, exact 0.95 d, approx Fig. 5. Active constraint types for a range of maximum aowed votage steps, with variabe power factors. -3 g21 g23 g26 strict votage step constraints has a significant negative impact on the amount of DG capacity that may be accommodated, more so than an equivaent imit on votage rise. Votage step constraints are most significant at agging power factors when the active and reactive power fow contributions reinforce each other. It has been shown that operation at eading power factor aeviates both votage and votage step constraints aowing greater voumes of DG to connect. However, as progressivey wider step change imits are aowed, more network capacity becomes avaiabe. The exact votage step mode, which incudes generator outage contingency power fow constraints in the OPF adds significanty to the computationa overhead (incuding n c contingency fows mutipes the size of the OPF mode by approximatey n c + 1.) The possibiity of using the simper two bus mode from Section II as an approximate method of enforcing votage step constraints has been examined as a means of reducing the computationa burden. The approximate expression for the votage step given in (2) was evauated using as inputs the impedances of the network from buses 21, 25 and 26 to the grid suppy point at bus 6, and the fixed power factor active and reactive power injections for the optima DG capacities in Fig. 3. The approximation was found to be fairy good at agging and unity power factor. However, as Fig. 6 shows, its performance at eading power factor is poor with, for exampe, the sign of the votage step on oss of generator 23 incorrecty predicted. This is because the active and reactive power fows have opposite signs but simiar magnitudes, which magnifies the reative error. As eading power factors are ikey to provide the optima capacity where step constraints are significant, the fu contingency approach demonstrated here wi therefore be necessary. This paper has been primariy motivated by the assessment of network generation capacity, with one additiona appication being to consider whether a proposed DG project wi adversey affect the capacity of the network to host DG esewhere. The Lagrange mutipiers of the various constraints coud guide panning decisions, by giving guidance as to where the greatest benefit can be obtained from the reaxation of votage and therma constraints [41]. It must be remembered Fig. 6. Comparison of the exact votage steps at the generator buses with the two bus approximation from Section II. Soid ines denote the exact approach, and dotted ines the approximate approach. In each case the optima generator capacities with a votage step imit of 3% are used. however that Lagrange mutipiers ony give the effect of margina constraint reaxations; as a constraint is reaxed further, another may become active and prevent further benefit. Beyond this particuar appication, this paper provides an exampe of the fexibiity of the OPF approach to network generation capacity assessment. Within an appropriate optimisation modeing environment, a variety of additiona technica constraints may be impemented in a fairy straightforward manner, by incuding contingency power fow constraints in an security-constrained OPF-ike manner. VI. CONCLUSIONS The votage step change that occurs on the sudden disconnection of a distributed generator an area of concern for distribution network operators. To expore how votage step imits infuence the amount of DG that can be connected within a distribution network, votage step constraints have been incorporated in a nove way within an estabished OPFbased method for determining the capacity of the network to accommodate DG. The assessment shows that enforcement of reativey strict votage step constraints has a significant impact on the amount of DG capacity that may be accommodated, more so than an equivaent imit on votage rise. Votage step constraints have the greatest impact at agging DG power factors when the active and reactive power fow contributions reinforce each other, whie operation at eading power factor tends to aeviate both votage and votage step constraints. It has been demonstrated that where progressivey wider step change imits are aowed, there is significant benefit in enabing greater amounts of DG to connect. A. Base Case OPF APPENDIX A FULL OPF FORMULATION A new generators n N are assumed to be avaiabe.

8 7 1) Objective function - maximise new DG capacity (MW): max p n, (5) n N where p n is the rea power capacity of new generator n, and N is the set of a new generators. 2) Capacity constraint for DG (MW): p n p n p + n n N (6) p ± n are the upper and ower imits on the capacity of new generator n. 3) Grid Suppy Point: Within this test exampe, there is a singe GSP of unimited capacity; hence, the grid suppy variabes p X x and qx X are unrestricted in range. The GSP wi be the sack bus in the power fow modes, and hence its votage phase is to be zero: δ βgsp = 0, (7) where the ocation of the GSP is β GSP. 4) Bus votage eve constraint: V b V b V + b b B (8) V b is the votage eve at bus b for the base-case power fow (i.e. a generators connected). V ± b are the upper and ower votage imits at bus b, and B is the set of buses. 5) Kirchhoff votage aw (KVL) - ines: At two termina buses for ine (denoted β 1 and β 2 ) the active and reactive power injections onto the ine are given in terms of votage eves and phases by the standard KVL formua. At bus 1, the active (f 1,P ) and reactive (f 1,Q ) injections are given by: f (1,2),(P,Q) f 1,P = g V (β 1 ) 2 V (β 1 )V (β 2 ) [ g cos ( δ(β 1 ) δ(β 2 ) ) +b sin ( δ(β 1 ) δ(β 2 ) )] (9) f 1,Q = b V (β 1 ) 2 V (β 1 )V (β 2 ) [ g sin ( δ(β 1 ) δ(β 2 ) ) b cos ( δ(β 1 ) δ(β 2 ) )] (10) are the rea (P ) and reactive (Q) power injections onto the two connection buses (1, 2) of. g and b are respectivey the conductance and susceptance of ine. The active and reactive equations for injection at bus β 2 may be obtained by transposing the abes 1 and 2 in (9) and (10). These constraints must be appied for a ines in L, the set of a ines. 6) Kirchhoff votage aw - transformers: These are identica in form to the KVL constraints for ines, except that the primary votage must be divided by the transformer tap ratio τ t. For instance, the KVL expression for rea power injection at the primary: f 1,P t = V β1 τ V β1 τ 2 g t (11) V β 2 [g t cos(δ β1 δ β2 ) + b t sin(δ β1 δ β2 )] The primary and secondary buses are denoted 1 and 2 respectivey, and the injections defined as for the ines. These constraints must be appied for a transformers t in T, the set of a transformers. 7) Tap ratio imit: τ t τ t τ + t t T (12) where τ t ± are the upper and ower imits on the tap ratio of transformer t. 8) Kirchhoff current aw: The sum of the grid suppy and generation at bus b is equa to the tota power injected onto ines and transformers pus the noda demand at b. b B, p X x + p n = p LT b + d P b (13) x X b n N b L qx X + (tan φ n )p n = qb LT + d Q b (14) x X b n N b L The terms (p, q) LT b are the sum of a power injections onto ines and transformers at b. The reactive power ine injection term incudes the capacitance term (V b) 2 b C + b C, 2 L β 1 =b L β 1 =b where b C is the shunt capacitance of the ine. 9) Fow imit constraints: Constraints on power injections at each end of ines, and the primary and secondary buses of transformers: (f (1,2),P ) 2 + (f (1,2),Q ) 2 (f + ) 2 L (15) (f (P,S),P t ) 2 + (f (P,S),Q t ) 2 (f t + ) 2 t T (16) B. Votage Reguation Constraints T b is defined as the set of transformers whose secondary bus is b, and which therefore reguate bus b. 1) Votage reguation constraint: For the resuts presented here, the votage of reguated buses is 1 p.u. in the base case power fow. This is formuated in the AIMMS optimisation environment as: V b = 1 {b B T b } (17) (the reguated buses are those where T b is not empty.) 2) Parae transformer constraint: A simpe mode for synchronised operation of transformers which reguate the same bus is to constrain their tap ratios to be equa: τ t1 = τ t2 b B, (t 1 t 2 ) T b (18) Aternativey, enforcing a maximum difference between the tap ratios woud be amost as straightforward. C. Transformer Outage Constraints The tota power fow across a pair of parae transformers is constrained beow the therma imits of each. (b B, t T b ), ( f 1,P t t T b ) 2 + ( f 1,Q t t T b ) 2 ( f t + ) 2 (19)

9 8 D. Generator Outage Contingency Constraints The foowing constraints are added to the mode for a generators n N to ensure that therma and votage step constraints are met on oss of a generator (here, contingency votage eve constraints are not enforced.) The symbos used are the same as before, except that the contingency power fow variabes are indexed by generator outage n. 1) Grid Suppy Point: The GSP is a (V, δ) bus which is enforced by the foowing constraints: δ c,bgsp = 0 (20) V n,b GSP = V bgsp (21) A other buses incuding oad and DG sites are (P, Q) buses. 2) Kirchhoff votage aw: The KVL expressions are identica to the base case except that contingency fow and votage variabes are used. As the votage step is defined before remedia action can be taken, the base case tap ratios τ t are used. 3) Kirchhoff current aw: b B, p X n,x + p n = x X b n N b n L qn X,x + (tan φ n )p n = x X b n N b n L p LT n,b + d P b (22) q LT n,b + d P b (23) 4) Fow imit constraints: These take the same form as the base case ines and transformers apart from the presence of contingency fow variabes, e.g. (f 1,P n, )2 + (f 2,Q n, )2 (f + ) 2 L (24) Here, it is assumed that the contingency therma imits are the same as those for the intact network but higher emergency ratings can be used. 5) Votage step constraint: V b V S,+ V n,b V b + V S,+ n N, (25) where V S,+ is the votage step imit. APPENDIX B TEST NETWORK PARAMETERS [19] A parameters are in per unit on a 100 MVA base. A. Loads Bus d P b d P b B. Line Impedances and Therma Limits (f + ) Line R X B c f C. Transformer Impedances and Therma Limits (f + t ) Transformer R t X t f t ACKNOWLEDGMENT The authors are gratefu for vauabe discussions with K. McKinnon and their partners in the AMPerES project, and to Ye Shouxiang for his efforts in advancing areas of this research in his MSc dissertation. REFERENCES [1] P. Barker and R. De Meo, Determining the impact of distributed generation on power systems. i. radia distribution systems, IEEE Power Engineering Society Summer Meeting, vo. 3, pp , [2] N. Jenkins, R. Aan, P. Crossey, D. Kirschen, and G. Strbac, Embedded Generation. Institution of Eectrica Engineers, [3] H. L. Wiis and W. G. Scott, Distributed power generation: panning and evauation. Marce Dekker, [4] A. Girgis and S. Brahma, Effect of distributed generation on protective device coordination in distribution system, Large Engineering Systems Conference, pp , [5] C. L. Masters, Votage rise: the big issue when connecting embedded generation to ong 11 kv overhead ines, IET Power Eng., vo. 16, no. 1, pp. 5 12, Feb [6] R. A. Waing, R. Saint, R. C. Dugan, J. Burke, and L. A. Kojovic, Summary of distributed resources impact on power deivery systems, IEEE Trans. Power Deivery, vo. 23, no. 3, pp , Juy [7] G. W. Aut and J. R. McDonad, Panning for distributed generation within distribution networks in restructured eectricity markets, IEEE Power Engineering Review, vo. 20, no. 2, pp , Feb [8] R. C. Dugan, T. E. McDermott, and G. J. Ba, Panning for distributed generation, IEEE Industry Appications Magazine, vo. 7, no. 2, pp , Mar.-Apr [9] P. Chiradeja and R. Ramakumar, An approach to quantify the technica benefits of distributed generation, IEEE Trans. Energy Convers., vo. 19, no. 4, pp , Dec [10] L. F. Ochoa, A. Padiha-Fetrin, and G. P. Harrison, Evauating distributed generation impacts with a mutiobjective index, IEEE Trans. Power Deivery, vo. 21, no. 3, pp , Juy [11], Time-series based maximization of distributed wind power generation integration, IEEE Trans. Energy Convers., vo. 23, no. 3, pp , Sept [12] C. Wang and M. Hashem Nehrir, Anaytica approaches for optima pacement of distributed generation sources in power systems, IEEE Trans. Power Syst., vo. 19, no. 4, pp , Nov [13] N. Acharya, P. Mahat, and N. Mithuananthan, An anaytica approach for dg aocation in primary distribution network, Int. J. Eectr. Power Energy Syst., vo. 28, no. 10, pp , Dec [14] A. Sivestri, A. Berizzi, and S. Buonanno, Distributed generation panning using genetic agorithms, Proc. IEEE Power Tech, pp. 257, [15] G. Cei and F. Pio, Optima distributed generation aocation in mv distribution networks, Proc. 22nd IEEE PES Internationa Conference on Power Industry Computer Appications, pp , [16] L. F. Ochoa, A. Padiha-Fetrin, and G. P. Harrison, Time-series based maximization of distributed wind power generation integration, IEEE Trans. on Energy Convers., vo. 23, no. 3, pp , Sept [17] A. Keane and M. O Maey, Optima utiization of distribution networks for energy harvesting, IEEE Trans. Power Syst., vo. 22, no. 1, pp , Feb [18] N. S. Rau and Y.-H. Wan, Optimum ocation of resources in distributed panning, IEEE Trans. Power Syst., vo. 9, no. 4, pp , Nov 1994.

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Distrib., vo. 1, no. 2, pp , March Chris Dent (M 08) is a Research Feow in the Schoo of Engineering at the University of Edinburgh, U.K. He obtained his B.A. degree in Mathematics from Cambridge University in 1997, PhD in Theoretica Physics from Loughborough University in 2001, and MSc in Operationa Research from the University of Edinburgh in His current research interests ie in efficient agorithms for arge scae optima power fows, network generation capacity assessment, and network reiabiity assessment. Dr. Dent is a Chartered Physicist and a member of the Institute of Physics, the Institution of Engineering and Technoogy, and the Operationa Research Society. Luis F. Ochoa (S 01, M 07) received the graduate from the Nationa Engineering University (UNI), Lima, Peru, in He obtained the M.Sc. and Ph.D. degrees from Sao Pauo State University (UNESP), Iha Soteira, Brazi, in 2003 and 2006 respectivey. He is currenty a Research Feow in the Institute for Energy Systems, Schoo of Engineering, University of Edinburgh, U.K. His current research interests incude distribution system anaysis and distributed generation. Dr. Ochoa is a member of the Institution of Engineering and Technoogy (IET) and CIGRE. Gareth P. Harrison (M 02) is a Senior Lecturer in Energy Systems in the Schoo of Engineering, University of Edinburgh, U.K. His research interests incude network integration of distributed generation and anaysis of the impact of cimate change on the eectricity industry. Dr. Harrison is a Chartered Engineer and member of the Institution of Engineering and Technoogy.