Long-Run Incremental Costs (LRIC) – Voltage Network Charges for Existing Network SVCs

Long-Run Incremental Costs (LRIC) – Voltage Network Charges for Existing Network SVCs

E. Matlotse1, E.T. Rakgati 2 and T. Kekgathetse 3

1 Senior Lecturer in the Dept. of Electrical Engineering, University of Botswana

2 Senior Lecturer in the Dept. of Electrical Engineering, University of Botswana

3 Final Year Student in the Dept. of Electrical Engineering, University of Botswana

Abstract

A novel approach is introduced whereby the original LRIC voltage network charging principle is modified and used to price for the existing network SVCs. Initially, this approach was used to price for the future network SVCs and in the process failing to cater for the existing network SVCs as it depicted its strength from varying network nodal voltages. To that end, the SVC VAr minimum limit was mapped to the network lower nodal voltage limit while the SVC VAr maximum limit was mapped to the network upper nodal voltage limit. Finally, the present SVC VAr loading capacity was duly translated to a corresponding voltage level within the context of the mapping exercise. The most attraction with this novel approach is that it offers forward-looking efficient economic signals which reflect the true burden on the existing network SVCs. Moreover, it penalizes those network users who advance the investment horizons of the existing network SVCs and otherwise incentivize those that defer the investment horizons of the existing network SVCs. This novel charging methodology is demonstrated on the IEEE 14 bus network.

1. Introduction

   Currently, in the new electrical power industry order, where deregulation and privatization is the number one priority, one of the key requirements is that the network operators should maintain the statutory required standard of network security and quality of supply at all times. One of the ways to achieve that is to always ensure that the network nodal voltages are within the required preset levels. In turn, the associated network charges should exactly reflect the true burden in the network in the context of the extent of the use of associated network assets (e.g. VAr compensation assets) under all prevailing conditions [1].

   In this regard, reactive power is the parameter to be utilized throughout the entire network to ensure that the network voltage profile is within the required limits. Reactive power can correctly classified as a resource that supports real power shipment, supplies reactive loads and reserve for maintaining voltage profiles under steady state and following credible contingencies. In a nutshell, network operators are required to secure adequate reactive power support to assist real power shipment to maintain the required level of network security and reliability. The reactive power resource in a network comes from three sources: 1) generators that produce reactive power 2) networks for carrying and generating reactive power for maintaining the security and quality of supply 3) suppliers who affect consumers reactive power consumption [2]. Most research in reactive power pricing [3]-[14] reflects the benefits from the first source generation, reflecting the operational cost related to reactive power due to new customers, i.e. how they might affect network losses. Network reactive power pricing also generates significant research interests into methodologies to reflect investment costs incurred in network when supporting nodal real and reactive power injection/withdrawal [2], [15]-[34], but the network investment costs are restricted to the circuits and transformers triggered by thermal limits. The first approach to charge for the cost of supporting network voltages [35] was developed and associated research was carried-out in [36] [40] as the approach evolved and propagated. However, all these [35] [40], fail to charge for the use of existing network SVCs and only charge for future network SVCs.

   This paper is concerned with development of network charges that account for the use of existing network SVCs. This charging principle employs the use of the unused nodal voltage capacity or headroom within an existing network to gauge time to invest in reactive power compensation device for each node in the system. A nodal withdrawal/injection of reactive power will impact on the nodal voltage, which in turn impact on the time to reinforce reactive power compensation devices. LRIC-v network charges are the

   difference in the present value of future Var compensation devices with and without the nodal perturbation, providing an economically efficient forward-looking pricing signal to influence the siting and/or reactive power consumption of demand and generation for bettering network voltage profile. This aforementioned LRIC-v network charging principle was modified to be able to be used to price for the use of the existing network SVCs. This owes to the fact that an SVC would be usually preset to a certain voltage level so as to maintain a constant voltage level at the bus at which it is sited. Given that the pricing approach in question depicts its strength from varying nodal voltage and unless a modification to it was effected, this approach would not apply in this case. It should be noted that an SVC while maintaining a constant network nodal voltage would have to supply or draw varying reactive power to or from the network to accomplish its mission. It was then this varying reactive power character by the SVC that was used, in that, the SVC VAr minimum limit was mapped to the network lower nodal voltage limit and the VAr maximum limit mapped to the network upper nodal voltage limit, at the bus this particular SVC was sited. Finally, the present SVC VAr loading was duly converted to a corresponding voltage level in the

   context of the mapping exercise. The above mentioned

   reinforcement consequent to voltage with and without the nodal increment

   In this section, the nodal base LRIC-V network charging principle formulation would be outlined. Thereafter, the formulation to reflect the nodal voltage impact on buses resulting from N-1 contingencies would be shown. Finally, this effect of N-1 contingencies would be factored into the former charging principle to constitute CF (contingency factor) LRIC-voltage network charges.

   1. Base LRIC-Voltage Network Charging Principle

      The following steps outlined below can be utilized to implement this charging model:

      1. Evaluating the future investment cost of network VAr compensation assets to support existing customers

         If a network node b, has lower voltage limit, VL and upper voltage limit VH, and holds a voltage level of Vb , then the number of years for the voltage to grow from Vb to VL /VH for a given voltage degradation rate vr can be evaluated from (1.a) or (1.b).

         If VL is critical, i.e, bus voltage is less than target voltage, 1 pu :

         mapping exercise is detailed in section 2.

         V V (1 v ) nbL

         (1.a)

         This paper is organized as follows: Section 2 details the mathematical models of the LRIC-voltage network charging and the mapping of SVC VAr limits to network nodal voltage limits. Section 3 covers the

         L b r

         On the other hand if VH is critical, i.e, bus voltage is more than target voltage, 1 pu :

         implementation of this principle and the resulting LRIC

         V V (1 v )nbH

         (1.b)

         voltage network charges to price for existing network SVCs. The papers conclusions are drawn in Section 4. Section 5 provides for Appendix which outlines the loading condition of the test system while References are depicted in Section 6.

         H b r

         where: nbL and bH are the respective numbers of years that takes Vb to reach VL /VH .

         Reconfiguring equations (1.a) and (1.b) constitute:

2. Mathematical Formulation of Long-Run Incremental Cost Pricing Based on Nodal Spare Capacity

   The LRIC-V network charging principle is based

   (1 v )nbL VL

   V

   V

   r

   r

   b

   (1 v ) nbH VH

   r V

   (2.a)

   (2.b)

   upon the premise that for an assumed nodal generation/load growth rate there will be an associated rate of busbar voltage degradation. Given this

   b

   then the values of nbL / nbH are

   assumption the time horizon for a busbar to reach its

   log V log V

   upper /lower voltage limit can be evaluated. Once the

   limit has been reached, a compensation device will be placed at the node as the future network reinforcement

   nbL

   bH

   bH

   n

   L b

   log(1 vr )

   log VH log Vb

   (3.a)

   (3.b)

   to support the network voltage profiles. A nodal demand/generation increment would affect the future investment horizon. The nodal voltage charge would then be the difference in the present value of the future

   log(1 vr )

   The assumption is that when the node is fully loaded the reinforcement will take effect. This means that

   investment will be effected in nbL /nbH years when the node utilization reaches VL /VH , respectively. At this point an installation of a VAr compensation asset is

   regarded as the future investment that will be needed at

   then the new present values of the future investments are

   the node to support the voltage.

   1. Determining the present value of future investment cost

   For a given discount rate of d, the present value of the future investment in nbL / nbH years will be:

   PVbnewL

   PVbnewH

   AssetCbL

   (1 d )nbnewL

   AssetCbH

   (1 d )nbnewH

   (7.a)

   (7.b)

   PV AssetCbL

   (4.a)

   The changes in the present values as consequent of

   bL (1 d )nbL

   the nodal withdrawal/injection QIn are given by (8.a)

   PVbH

   AssetCbH

   (1 d )nbH

   (4.b)

   and (8.b)

   PVbL PVbnewL PVLb

   (8.a)

   where AssetCbL and AssetCbH are the modern equivalent asset cost to cater for supporting voltage due to lower voltage limit and upper voltage limit violations,

   respectively.

   PVbH

   PV

   bnewH

   • PVbH

     (8.b)

     3). Deriving the incremental cost as a result of an additional power injection or withdrawal at node N

     If the nodal voltage change is VbL / VbH consequent

     The annualized incremental cost of the network items associated with component b is the difference in the present values of the future investment due to the

     reactive power magnitude change Q at node N

     upon an additional QIn withdrawal/injection at node N,

     In

     multiplied by an annuity factor

     this will bring forward/delay the future investment from year nbL/nbH to nbnewL /nbnewH and when VL is

     IVbL PVbL * annuityfactor

     (9.a)

     critical

     for withdrawal

     VL (Vb

   • VbL

     ) (1 v )nbnewL

     (5.a)

     IVbH

     PVbH

     * annuityfactor

     (9.b)

     r

     r

     or

     for injection V (V V ) (1 v )nbnewL

     (5.b)

     4) Evaluating the long-run incremental cost

     If there are a total of bL busbars lower limits and

     L b bH r

     and when VH is critical

     bH busbars high limits that are affected by a nodal increment from N, then the LRIC-V network charges at

     for withdrawal VH (Vb VbL ) (1 v ) bnewH

     n

     r

     r

     or

     (5.c)

     node N will be the aggregation of the changes in present value of future incremental costs over all affected nodes:

     for injection VH (Vb VbH ) (1 v ) bnewH (5.d)

     n

     r

     r

     IV

     IV

     LRIC _V

     bL bL

     (10.a)

     Equations (6.a), (6.b), (6.c) and (6.d) give the new investment horizons as

     N , L

     QIn

     nbnewL

     log VL log(Vb VbL ) log(1 vr )

     (6.a)

     LRIC _VN , H

     bH IVbH

     QIn

     (10.b)

     nbnewL

     or

     log VL log(Vb VbH ) log(1 vr )

     (6.b)

     1. Mapping SVC Limits to Network Nodal Voltage Limits

     Since the existing network SVC is meant to continuously adjust its reactive power output to

     nbnewH

     log VH log(Vb VbL ) log(1 vr )

     or

     (6.c)

     regulate the voltages at the controlled bus to a preset value (e.g. 1 pu), therefore, the bus voltage at which this SVC exists remain constant and, only, the devices

     reactive power output varies accordingly. Owing to this

     nbnewH

     log VH log(Vb VbH ) log(1 vr )

     (6.d)

     factor, the LRIC-voltage network charging approach can not be applied without any modification, therefore,

     this aforementioned approach is modified as detailed below to accommodate the behaviour of the existing network SVC.

     If a network node b , has a lower voltage limit, VL and an upper voltage limit, VH , and on this bus if there exist an SVC having minimum reactive power capacity, Qmin and maximum reactive power capacity, Qmax. Then Qmin can be mapped to VL while Qmax can be mapped to VH and, therefore, the relation below by equation (11) holds

     test network is assumed to be 1.6% while the discount rate is assumed to be 6.9%.

     Also, on the above test system, there are two SVCs, one existing at bus 4 and the other at bus 12. These SVCs were randomly installed to exist at these respective buses. It is emphasized that, the reactive power planning (RPP) exercise determines the optimal allocation of VAr compensation assets through-out the entire power system to ensure network security and reliability at the least possible costs. To this end, it can

     VH VL

     (11)

     be said that, the random existence of SVCs at the

     V V

     VH

     2

     Q Q

     aforementioned buses is just meant to demonstrate the

     V H

     L Q

   • max min

     bSVC

     2

     Q Q

     gen

     2

     Q

   • max min

   concept of charging for the use of these existing

   max

   2

   network SVCs.

   Both the SVCs at buses 4 and 12 have the same

   With the mapped voltage VbSVC known, then Vb in equations ((1) (3)) and ((5) (6)) can be replaced by the voltage to price the contribution of the existing network SVC at the node where it is sited.

3. Implementation

   1. Test System

      13

      specification of maximum and minimum VAr capabilities of 100 MVAr and -50 MVAr, respectively. Both these SVCs have their voltages preset at 1 pu, so as the voltage settings for synchronous condensers at buses 3, 6 and 8. The nodal lower and upper voltage limits remain to be 0.94V and 1.06V, respectively.

   2. LRIC-Voltage Network Charges to Price for Existing Network SVCs

      Figure 2 shows the 1 MVAr nodal withdrawals to

      17 km

      12

      11 km

      5 km 11

      14 km

      10

      6 km

      14

      9 km

      reflect the LRIC-V network charges for the use of these existing network SVCs. On the other hand, Figure 3 shows the 1 MVAr injections to reflect the LRIC-V

      6 km

      G

      1 C 6

      2 km

      9

      8 C

      7

      network charges for the use of the above mentioned existing network SVCs.

      82 km

      13 km 4

      5

      38 km

      G GENERATORS 2

      C SYNCHRONOUS COMPENSATOR

      56 km 62 km

      G 70 km

      64km

      3

      C

      Fig. 1: IEEE 14 Bus System

      The test system shown above in Fig. 1 is the IEEE 14 bus network, the load and generaton data of this network are shown in the appendix section. This network consists of 275kV subtransmission voltage level shown in red and the 132kV distribution voltage level shown in blue. There are two generators and three synchronous compensators as depicted in the diagram. The line distances between the buses are depicted in blue and red for the subtransmission and distribution levels, respectively. The compensation assets (SVCs) have the investment costs of £1, 452,000 and £696, 960 at the 275-kV and 132-kV voltage levels, respectively. Bus 1 is the slack bus. The annual load growth for this

      Fig. 2: LRIC-voltage network costs resulting from 1 MVAr nodal withdrawals to reflect the use of existing network SVCs

      It should be noted that, the initial VAr loadings of SVCs at buses 4 and 12 were 40.987 MVAr and

      11.365 MVAr, respectively. These VAr loadings translated to 1.013V and 0.989V for buses 4 and 12, respectively, owing to the SVC VAr limit/nodal voltage limit mapping exercise. In this regard, during nodal withdrawals, bus 4 was attracting a cost since reactive power had to be injected into the network and that represented a voltage increase in the mapping exercise context and, therefore, a degradation of this bus upper

      voltage limit margin. This latter effect meant the investment horizon of the concerned SVC was brought closer and, therefore, a penalty imposed in the context of a cost. On the other hand, for bus 12, the reverse was true and hence a credit during nodal withdrawals as its already critical bus lower voltage margin (voltage from the context of transforming node SVC VAr loading to node voltage) is increased and, therefore, its investment horizon was deferred as a result.

      Specifically, during 1 MVAr nodal withdrawals, it can be observed that buses 3, 6 and 8 attract no charges as the synchronous condensers at these buses absorbed all the shock resulting from these particular withdrawals, by supplying reactive power into the network. However, bus 2 attracts a cost even though a generator is connected at this bus since this connected device has reached its VAr capacity. It can be observed that bus 4 attracts the most cost as during MVAr withdrawal at this bus, the existing SVC there makes up all for the withdrawal. Elsewhere, other than buses 12 and 13, the costs reduce as these buses distances from bus 4 increase, owing to the reduced perturbations impacted on bus 4 and increased perturbations impacted on bus 12 which is attracting credits. On the other hand, bus 12 attracts a credit since it absorbs all the impact resulting from the withdrawal on it. Bus 13 also attracts a credit, since, due to its closeness to bus 12, during MVAr withdrawal at the former bus the voltage at the latter bus is offset only to be restored by the action of the SVC at bus 12 in putting more capacitive reactance into the network.

      Fig. 3: LRIC-voltage network costs resulting from 1 MVAr nodal injections to reflect the use of existing network SVCs

      In the contrary, during nodal injections, buses 4 and 12 attract credit and cost, respectively. The trend in this case is the same as the earlier case but in the opposite sense. The same reasons as advanced above hold in this case and, therefore, for MVAr nodal injections bus 4 attracts the most credit while buses 12 and 13 attract costs.

4. Conclusions

   This paper presents a novel long-run incremental cost (LRIC) pricing principle to price the use of existing network SVCs. The original principle is premised upon the spare nodal voltage capacity of an existing network to reflect the impact to the network wide voltage profile and the cost of future network VAr compensation consequent upon a nodal injection/withdrawal, i.e. whether they accelerate or delay the need for future network compensation devices. The model is thus cost-reflective and able to provide forward-looking economic signals to influence network users behavior in order to minimize the cost of future investment in VAr compensation. The original LRIC-voltage network pricing principle was unable to price for the use of existing network SVCs in its original form. Therefore, the original pricing approach was modified, in that, the SVC VAr minimum limit was mapped to the network lower nodal voltage limit while the SVC VAr maximum limit was mapped to the network upper nodal voltage limit. Finally, the present SVC VAr loading level was translated to the corresponding voltage level within the context of the already mentioned mapping exercise.

   This study was carried-out on a 14-bus network. The major findings from the demonstrations are summarized as follows:

   1) This novel network pricing principle reflects both the true burden on the existing network SVCs and the associated indicative forward-looking economic signals.

   2). This pricing approach penalizes those network users who advance the investment horizons of the existing network SVCs and, otherwise, incentivize those that defer the investment horizons of the existing network SVCs.

   The next phase would be to integrate this pricing approach with the one for pricing for future network VAr compensation assets following the reactive power planning (RPP) exercise.

5. Appendix

   The used IEEE 14 bus network is described in detail in [41]. The loading and the generation conditions of this used network are shown below in Tables 1 and 2, respectively.

   Table 1. IEEE 14 Network Load Data

   Bus	MW	MVAr
   1	0	0
   2	21.7	12.7
   3	94.2	19
   4	47.8	-3.9
   5	7.6	1.6
   6	11.2	7.5
   7	0	0
   8	0	0
   9	29.5	16.6
   10	9	5.8
   11	3.5	1.8
   12	6.1	1.6
   13	13.5	5.8
   14	14.9	5

   Table 2. IEEE 14 Generator Data

   Bus	Real Power(MW)	Max VAr(MVAr)	Min Var(MVAr)	Voltage pu
   2	40	50	-40	1.045
   3	0	40	0	1.01
   6	0	24	-6	1.07
   8	0	24	-6	1.09

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   1. Furong Li and E. Matlotse, Long-Run Incremental Cost Pricing Based on Nodal Voltage Spare Capacity, IEEE Power and Energy Society General Meeting, pp. 1 5, 20-24 July 2008.

   2. Matlotse E. and Furong Li, Long-run incremental cost pricing for the use of network reactive power compensation devices for systems with different R/X ratios, IEEE PES General Meeting, pp. 1-8, 26-30 July 2009.

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7. Biographies

Edwin Matlotse was born in Taung, South Africa in 1969. He received BEng in Electrical and Electronic Engineering at the University of Botswana, Botswana, in 1995 and an MSc in Electrical Power at the Bath University, U.K., in 2001. Also, he earned a PhD

degree at the Bath University, Bath City, U.K., in 2011. His PhD degree topic was Long-Run Incremental Cost Pricing for Improving Voltage Profiles of Distribution Networks in a Deregulated Environment.

Currently, he is a senior lecturer at the University of Botswana in the department of Electrical Engineering. His major research interest is in the area of electrical machines, power system voltage study, analysis and power system economics.

Edward T. Rakgati as born in Mochudi (Botswana) on 03/12/1969. He Obatined BEng (Electrical and Electronics), MSc (Power Engineering & Drives) and Phd (Electric Machines and Drives)

from Botswana, UK and SA respectively. The degrees were obtained in 1996, 1998 and 2006 respectively. His research area includes computer aided design of Electric machines, Application of power electronics in machine control.

He has published in both local and international conferences/journals and journals in power engineering Dr. E.T. Rakgati is a member of both the Botswana institution of Engineers and the institution of Electrical Engineers (IEE).

Terrence Kekgathetse was born in Kanye, Botswana in 1990. He is currently pursuing his BEng in Electrical and Electronic Engineering at the University of Botswana. His bachelors degree topic is Forward-Looking

Economic Signal of Integrating Solar Power onto the Botswana Power Corporation (BPC) Grid.

His major research interest is in the area of power system analysis and power system economics.