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Optimal capacity planning of substation transformers by demand response combined with network automation
Electric Power Systems Research 134 (2016) 176–185
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Optimal capacity planning of substation transformers by demand response combined with network automation Muhammad Humayun a,∗ , Amir Safdarian b , Mubbashir Ali a , Merkebu Z. Degefa a , Matti Lehtonen a a b
Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland Department of Electrical Engineering, Center of Excellence in Power System Control and Management, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 13 August 2015 Received in revised form 10 January 2016 Accepted 13 January 2016 Keywords: Automation Planning Demand response Substation Transformer
a b s t r a c t The inclusion of smart grid features such as demand response (DR) and network automation for capacity planning of substation transformers may provide substantial monetary savings. This paper proposes an optimization model for quantification of the savings in capacity management of substation transformers over long-run. The proposed model incorporates the DR as a resource to decrease the outage cost during contingencies while considering existing switching types for load transfer between substations. The model provides optimal selection and scheduling of multistage transformer installations and their refurbishments by considering all the costs associated with them including investment, losses, maintenance, reliability, and the salvage value. For a realistic study, numerical value of the savings in transformers’ cost is calculated for a typical Finnish two-transformer primary distribution substation planning over a period of forty years. Case studies are performed based on situations encountered by utilities and type of load transfer switching (manual and remote) between substations. A sensitivity analysis based on DR penetration and load curtailment (LC) cost is also performed. The results indicate that substantial monetary benefits can be obtained in substation transformers’ cost by utilities through employing DR. The benefit of DR is superior for cases where it is used in combination with remote switching of load transfer between neighbouring substations (NSS). © 2016 Elsevier B.V. All rights reserved.
1. Introduction Smart grid features offer new opportunities for improving practices of the asset management in the future power systems. Demand response (DR) and network automation are the most critical features among others as they have impact on the load profile at feeders and transformers. Substation transformers, the most costly components in a distribution system, can gain substantial increase in their utilization efficiency by using these techniques [1–7]. These utilization gains may be obtained by activating DR and/or transferring load to neighbouring substations (NSS) following a contingency, thus releasing the reserve capacity for normal operation usage [2–7]. This reserve capacity is kept, due to conventional design requirements (e.g., N − 1), to provide support during contingencies which are rare events. The best time to consider DR for substation transformer capacity management is at the planning phase as extra investments in the
∗ Corresponding author. Tel.: +358 50 415 4331. E-mail address: muhammad.humayun@aalto.fi (M. Humayun). http://dx.doi.org/10.1016/j.epsr.2016.01.011 0378-7796/© 2016 Elsevier B.V. All rights reserved.
assets may be avoided resulting into higher utilization efficiency over their entire lifetime. This can be confirmed by the European Directive 2009/72/EC [8] emphasizing that the DR should be considered during planning stage of the distribution system capacity. The existing load transferring switch types (e.g., manual and remote) can have a significant impact on DR based planning solution [5–7]. This is because the DR cannot provide load reduction for longer time as flexible appliances cannot be turned off for many hours [9] and after certain time DR payback/rebound load also appears in the load profile. Therefore, activating DR potentials and the existing switching type for load transfer to NSS should be considered in parallel in the planning. In the literature of substation transformer capacity planning, the possible impact of employing DR in the planning process of distribution networks has not been well examined. The research in this field has almost been limited to the effect of DR in operational planning of distribution system and transformer capacity [1–4], [10–12]. The authors evaluated the utilization efficiency improvement of substation transformers using DR in [1–4]. The impact of electric vehicle load on the secondary distribution transformers and their integration using DR was evaluated in [13–15]. The
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
Nomenclature Sets and indices h, z, indices of hour in a year z , z index for choices of transformer sizes i j, j indices for transformer locations in a substation t, t indices of year index for load level of demand LL LLm number of load levels M number of transformer locations N number of transformer size choices number of years of planning T Parameters cDR unit incentive paid to customers for using their DR flexibility cLC unit load curtailment cost discount rate (based on inflation and interest rates) d hsw switch time, its value depends upon the type of load transfer (i.e., manual or remote) between substations loss equivalent resistance of transformer on location rjt j at year t y decrease in equivalent age of a transformer due to a maintenance action Ci procurement cost of transformer size i DLL duration of load level LL emergency rating multiplier of a transformer ER NLtj no-load loss of transformer on location j at year t NSSt PCt,z t,z PDR
t,z,z PDR t PEng,LL PWt max TDR Tr i
t i,j
jt , jt jt
DRz,z j,t,h
load deferred from hour z to later hour z
DRj,t,h
load deferred to z in prior hours z
LCzj,t,h
current flowing through transformer at location j, load level LL, and year t amount of critical load curtailed
z ,z
t Ij,LL
LOLtj,ini
LOLtj,rep NLtj z Pj,t,h PWC PWCtInt PWCtInv PWCtLoss PWCtMai PWCSal TECtj TLOLj
available flexible load at year t, hour z
TLOLj,ini
peak bound of variable for load deferred from hour z to later hour z energy price at load level LL and year t present worth factor of costs at year t maximum time for which a load can be deferred repair time of a transformer general symbol for parameters (of capacity, cost, resistance, and no-load of loss of transformer) of size i
dependent variables; unity value indicates that replacement transformer are in service dependent variables dependent variables; unity value indicates that initial transformer are in service decision for refurbishment of transformer at location j and year t
Continuous variables maintenance cost of transformer at location j and mctj year t age of transformer at location j and year t Atj ini CInv rep CInv
Capj ,ini Capj ,rep DRzj,t,h
investment cost of the transformer at j investment cost of initially selected transformer at location j capacity of initial transformer at location j capacity of replacement transformer at location j demand deferred under demand response
neighbouring substation capacity at year t available critical load at year t, hour z
Binary variables bti,j decision for selection of a transformer size as a replacement fbi,j decision for selection of a particular transformer i as initial transformer at location j t ˇi,j dependent variables ˇjt , ˇjt
Cj Cj,ini
investment cost of initial transformer investment cost of replacement transformer
177
TLOLj,rep j,ini
j,rep
tj
loss-of-life of initial transformer at location j and year t loss-of-life of replacement transformer at location j and year t no-load loss of transformer on location j at year t modified load profile after overload relieving actions total present value of costs of transformers in a substation present value of interruption/reliability cost at year t present worth of the investment cost at year t present worth of losses cost at year t present worth of maintenance cost at year t. present worth of salvage value of investments emergency capacity of healthy transformers during contingency of transformer at location j and year t total accumulated loss-of-life of transformer existing at j by the end of the study period total accumulated loss-of-life of initial transformer at location j total accumulated loss-of-life of replacement transformer at location j parametric values (capacity, cost, resistance, and no-load of loss) for initial transformers at location j parametric values (capacity, cost, resistance, and no-load of loss) for replacement transformers at location j failure rate of transformer at location j and year t
benefit of DR for reliability improvement of distribution systems was assessed in [11,12], [16,17]. The impact of DR and automation on distribution system reliability cost was discussed in [18]. Studies [19,20] reported that overinvestments in transmission network capacity can be avoided using DR at the planning stage. In [21], the substation capacity planning was in conjunction with distribution system reinforcement in presence of DR, however, transformer maintenance scheduling, increasing failure rate with aging, salvage value based on insulation loss-of-life (LOL), and load transfer to neighbouring substation (NSS) during contingencies were not incorporated. The authors also presented an optimization model [22] for substation capacity planning, but NSS support and DR features were not considered. Therefore, an appropriate tool for quantification of DR benefits considering load transferring switch types in substation capacity planning is needed. In this article, the influence of DR along with type of switches for load transferring to NSS is investigated on the optimal capacity planning of transformers for a primary substation. The impacts of DR and load transferring time to NSS are appropriately included in outage cost calculation of the proposed optimization model for
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planning and management of transformer capacities in a substation. The optimization model accounts all the costs related with the transformers including investment cost, operational cost, reliability cost, and salvage value. In the optimization model, transformer increase in failure rate with age and salvage value based on the insulation LOL are also incorporated. The model decides the optimal selection of transformers’ sizes, their maintenance times, and stage of transformers replacements in the planning horizon in order to reduce the present worth of total cost to satisfy the given load. A simulation is developed to quantify the benefits of DR while considering load transfer switching times. Using the simulation, numerical results are obtained and analysed for capacity planning of a typical Finnish two-transformer primary distribution substation. Demand profile and DR capacity of the load are estimated by hourly measured consumption and survey data from central Finland. Case studies are performed based on situations encountered by utilities and load transfer switching types (i.e., manual and remote). A broad sensitivity analysis is also performed considering the variation in DR penetration of load and load curtailment (LC) cost. Numerical results indicate that the utilization of DR can provide substantial saving in total substation transformer costs. The savings are superior when combination of DR and remote switching are applied instead of DR with manual load transfer switching. This paper is organized as follows: Section 2 provides the DR capability related information. The optimization model is formulated in Section 3. The test system details are provided in Section 4. Section 5 describes the case studies’ results and discussion. The conclusions follow in Section 6. 2. Demand response capability This section provides the DR basics, DR potential of household appliances, and the method of determining DR capability of the load profile at the primary substation level. DR is defined as “changes in electricity usage by the end-use customers from their normal consumption pattern in response to changes in the price of electricity over time or when system reliability is jeopardized” [23]. Based on flexibility in operation, domestic electrical appliances are classified into two categories: controllable and critical. The operation of controllable appliances can be moved in time whereas critical appliances do not offer such flexibility in operation. It is worth mentioning that controllable loads are also referred to as responsive loads. Washing machines and dishwashers can offer flexibility in operation by delaying wash action and altering cycle duration. DR in clothes dryers can be realized by postponing its operation or by changing heating phase time. In cold appliances (refrigerator and freezer), DR can be achieved by deferring ice forming and defrost actions, modifying on-time cycle, and allowing slight temperature modifications during emergency
Table 1 Demand response potential of domestic appliances [25,26]. Appliance
DR potential (h)
Refrigerator/freezer/air conditioner/clothes dryer/direct space heating Storage water heater Washing machine Storage space heating/dish washer
1
3 4 5
periods. Similarly, heaters and air conditioners offer flexibility by rescheduling run time and altering temperature bounds within the limits set by users. The distinctive nature of heating loads, instigated by thermal inertia, makes them greatly responsive [24]. Table 1 lists the DR time shifting capacity of controllable appliances [25,26] considered in this article. Rest all the devices (television, personal computer, stove, lighting, etc.) are in the category of critical appliances. In order to determine the available DR capability of load at a particular time, along with flexibility of each appliance, the disaggregated load profile of controllable appliances is also needed. For that, a one year automatic meter reading hourly load data measured from 1600 residential consumers in central Finland is used to build the load profile of the transformers. Then, conditional demand analysis (a statistical regression technique) is applied to this metered data, weather information, and statistical data collected by survey [27] to achieve the demand disaggregation. The survey data contains the information related to houses, people living in them, and electrical appliances. The disaggregated load profile of a typical winter week-day for a typical house is shown in Fig. 1. Finally, average DR capability of demand is determined by using the disaggregated demand and DR values of appliances from Table 1, as obtained in [1,3]. 3. Problem formulation This section proposes a mixed integer quadratic programming (MIQP) optimization formulation for capacity management of substation transformers in presence of DR and NSS connection. Assume that a transformer can be installed on each transformer location at a substation from available choices in the beginning of planning phase. A new transformer from available choices can replace the current transformer at a later phase at each location. Furthermore, maintenance/refurbishment activities can be performed to decrease the failure probability of transformers. During the failure of transformers, load on healthy transformers can be reduced by activating DR, by transferring load to neighbouring substations (if there is free capacity), and/or by LC. The aim is to find a set of decision variables indicating transformers’ selection of ratings, stage
Fig. 1. Disaggregated load profile of a typical winter week–day for a typical house.
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
(year) of maintenance, and time of replacements in the planning horizon such that the total cost is minimized for the transformers. 3.1. Objective function The objective of optimization model is formulated as (1); the goal is to minimize total cost of transformers in a substation over the entire planning period. Minimize PWC =
T
PWCtInv + PWCtLoss + PWCtMai + PWCtInt
t=1
− PWCSal
(1)
where t and T are index of year and its maximum value, respectively. PWC is present worth of total cost of transformers in a substation. PWCtInv , PWCtLoss , PWCtMai , and PWCtInt are present worth of investments, losses, maintenance, and interruption/reliability costs at year t, respectively. PWCSal denotes the salvage value of investments. The details of each cost component are given in the following: (1) Investment cost: The investment cost of transformers depends on their ratings and internal design. In this paper, transformer costs of procurement, commission, and decommissioning are included in the investment cost. The investment cost of initial and replacement transformer installations is given by the following expressions. ini PWCtInv = CInv =
N M
Ci · fbi,j t = 1
(2)
j=1 i=1
rep
PWCtInv = CInv = PWt ·
N M
Ci · bti,j
∀t = 2, . . ., T
(3)
j=1 i=1
PWt =
1 (1 + d)
t−1
∀t
(4)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. Ci refers to the procurement cost of transformer size i. fbi,j and bti,j are binary decision variables denoting the selection of a particular size transformer at each location as initial and replacement installations, respectively. M and N denote total number of transformer location in the substation ini and C rep and number of transformer size choices, respectively. CInv Inv represent the cost of initial and replacement transformers, respectively. PWt is the present worth factor and d is the discount rate (based on inflation and interest rates). The investment cost at the beginning of planning horizon in (2) is sum of investment cost of first transformer installations at each location. The present worth of investment cost of replacement transformers in (3) depends on the size of replacements transformer and year of replacement. (2) Losses cost: Eq. (5) provides the yearly present worth cost of substation transformer losses. These losses cost depends upon the transformers’ winding loss, core loss, and energy price. PWCtLoss = PWt ·
M LLm j=1 LL=1
2
t ) · r t + NLt (Ij,LL j j
t ·DLL · PEng,LL
∀t
(5)
179
transformer which is calculated based on transformer rating, voltage, and load value. rjt and NLtj are transformer’s loss equivalent winding resistance and nominal no-load loss, respectively. DLL is t duration of a load level and PEng,LL is energy price. PWt and PWCtLoss represent the present worth factor and present worth of losses cost, respectively. As values of the transformer parameters (resistance and noload loss) depends upon the transformer selection made by the optimization model from various alternatives. Therefore, consistent values of these parameters should be considered in the calculation. These parametric values (resistance and no-load loss) of transformers required in (5) are calculated by the following equations:
j,ini =
N
i · fbi,j
(6)
i=1
j,rep =
N T
i · bti,j
(7)
t=2 i=1
tj = jt · j,ini + ˇjt · j,rep
∀t = 2, . . ., T
btj − ˇjt + ˇjt−1 = 0 ∀t = 2, . . ., T and btj =
(8) N
bti,j
(9)
i=1
−ˇjt+1 + ˇjt ≤ 0 ∀t = 2, . . ., T − 1
(10)
jt + ˇjt = 1 ∀t = 1, . . ., T
(11)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. N and T denote total number of transformer size choices and number of years of planning, respectively. fbi,j and bti,j are primary binary decision variables of transformer selection. , j , j,ini , and j,rep refer to the general symbol for transformer parameters (capacity, cost, resistance, and no-load loss), their value for initial, and replacement transformers, respectively. jt and ˇjt are dependent binary variables whose unity value indicates the initial and replacement installation of a transformer as in-service, respectively. Eqs. (6) and (7) are used to find the parametric values of initial and replacement transformers. The parameters of initial transformer selections are the values at the first year; however, either initial or replacement transformer can be present at later years. Therefore, (8)–(11) are utilized in order to determine the parameters of transformer installations for year 2 or later. Eqs. (9)–(11) guarantee that once an initial transformer is replaced by a new transformer at a location then unity value is allotted to ˇjt for all the future years. (3) Maintenance cost: Typically, the cost of maintenance inspections and actions is low; however, main refurbishments are of significant cost. In this manuscript, maintenance refers to these main refurbishment actions that decreases the failure probability of the transformers. The maintenance cost of transformers in a substation is determined by the following equation:
PWCtMai = PWt ·
M
jt · mctj
(12)
j=1
where j, LL, and t are the indices of transformer location, load level of demand, and planning year, respectively. M and LLm denote total number of transformer location in the substation and number of t denotes the current flowing through load levels, respectively. Ij,LL
where j and t are the indices of transformer location and planning year, respectively. M denotes the total number of transformer locations in the substation. jt is binary decision variable indicating
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an overhaul action at year t on location j. mctj is cost of maintenance whose value depends on the in-service transformer size which is determined by using (6)–(8). PWt and PWCtMai represent the present worth factor and present worth of maintenance cost, respectively. (4) Interruption/reliability cost: The present worth of yearly interruption cost of transformers is calculated by (13). It is determined by considering transformer failures while considering instance of failures, failure rates, load curtailed, and DR activated.
PWCtInt
t
= PW
8760 M
tj 8760
j=1 h=1
·
h+Tr
cLC · LCzj,t,h
+ cDR · DRzj,t,h
z=h
(13) where j, t, h, and z are the indices of transformer location, planning year, hour of a year, and hour of repair, respectively. M and Tr denote the total number of transformer locations in the substation and average repair time for transformers, respectively. LCzj,t,h and
DRzj,t,h are variables representing the amounts of load curtailed and demand deferred, respectively. cLC and cDR are unit cost of LC and DR, respectively. tj denotes the transformer failure rate per annum. In (13) at first, a transformer failure is assumed at an hour (h) in a year (t) for a particular transformer at location (j) in a substation. Then, outage cost is calculated for that contingency, which is the sum of load curtailment cost for critical load and load under DR during each hour of the repair duration. After that, this outage cost is multiplied by transformer failure probability at that hour in a year. Subsequently, outage cost of that transformer considering contingencies occurring at each hour of a year (8760 h) is summed. Similarly, outage costs of all the transformers at a substation are added. Finally, this summed outage cost is weighted by the present worth factor. As transformers loads are hourly varying and also DR potentials also are different at different hours, therefore, limiting substation load below their peak capacity require time varying optimal load alleviation decision. The decision variables of LC and DR activation are determined by the following equations:
∀z < h + hsw
z Pj,t,h ≤ TECtj
∀z ≥ h + hsw
z Pj,t,h ≤ TECtj +NSSt
(14) (15)
TECtj =
jt · Capj ,ini + ˇjt · Capj ,rep · ER
(16) Atj = jt ·
j =1,j = / j t,z z Pj,t,h = PDR + PCt,z +
z
,z DRzj,t,h − LCzj,t,h −
t,z 0 ≤ LCzj,t,h ≤ PDR + PCt,z +
DRz,z ≤ j,t,h
z
DRzj,t,h =
,z DRzj,t,h −
DRz,z j,t,h
(17)
DRz,z j,t,h
(18)
z
t,z,z max PDR ∀z < z andz ∈ z + 1, 2, . . ., TDR
(19)
z
max DRz,z ∀z < z andz ∈ z + 1, 2, . . ., TDR j,t,h
t t =1
z
z
,z max times z , and DRzj,t,h load deferred to hour z in prior times z . TDR is the maximum time for which a load can be deferred. Load at any time should not be greater than the sum of maximum allowed loading of the transformer. The constraints (14) and (15) bound the modified load profile after LC and DR activation within the defined capacity limits. During switching time (14), only available transformers’ capacity is emergency capacity of healthy transformers in the same substation because load transfer to neighbouring substations is being arranged. Whereas, NSS capacity is also available to support the load after switching times (15) as load transfer actions has already been conducted. Eq. (16) determines the emergency load carrying capacity of healthy transformers in the same substation which is the sum of capacity of healthy transformers multiplied by their emergency rating multipliers. The modified load profile during a contingency is determined by (17) which is the sum of available flexible load, critical load, load deferred in prior times minus load curtailed, and load deferred to later times. The third term on the right hand side of equality in (17) is for load recovery that was deferred in earlier hours. Eq. (18) defines the upper limit of LC that depends on flexible load, critical load, and prior and current DR decisions. The constraint (19) sets the limit of DR activation; the sum of load that can be postponed to a later time is limited to the sum of power available under DR contract. Eqs. (18) and (19) ensure that LC and DR do not cross their logical limits. Eq. (20) determines the total load deferred under DR at any time which is the sum of loads that are postponed to all possible future times. Utilities’ experience indicates that the failure rate of transformers increases with their age. Ref. [28] provides an exponential expression (21) for estimating the transformer increasing failure rate. The reasons of considering this growing rate of transformers in this model are to imitate real failure mechanism and significance of reliability/interruption cost in transformer replacement planning. The interruption cost directly depends on failure rate. Eq. (22) is used to calculate the age of transformers.
tj = f (Atj ) = 0.001 exp(0.0944 · Atj ) + 0.0169
M
and emergency load carrying capability of healthy transformers in a substation, respectively. ˇjt and jt are dependent binary variables. hsw is switching time of load to NSS whose value is selected based on the type of load transfer (i.e., manual or remote) between substations. Capj ,ini and Capj ,rep are capacity of initial and replacement transformers at location j , respectively. NSSt is NSS load receiving capability. LCzj,t,h is load curtailed, DRz,z is load deferred to later j,t,h
(20)
z
where z, z , and z are the indices of hour of year during transformer t,z z , PCt,z , and Pj,t,h are available flexible load, critical load, and repair. PDR modified load profile after LC and DR activation, respectively. ER and TECtj denote the emergency rating multiplier of transformers
jt − y · jt · jt
+ ˇjt ·
t
(21)
ˇjt − y · jt · ˇjt
(22)
t =1
where j is index of transformer location in the substation. t and t are indices of planning year. tj is failure rate of transformer, Atj denotes the number of years conceded since the transformer installation. ˇjt ,
ˇjt , jt and jt are dependent binary variables. jt and y are binary decision variable indicating an overhaul action at year t on location j and corresponding decrease in the age of transformer due to that maintenance action, respectively. The first summation term in (22) provides the value of Atj if the initial transformer installation is supplying the load, while the second summation term is utilized in case the replacement installation is in service during the present year. The second sub-term in each summation denotes the reduction in failure rate of transformers due to maintenance actions. (5) Salvage value: The salvage (residual) values of transformers at the end of planning period or at the time of retirement/replacement are calculated by (23)–(28). The first and second terms in (23)
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
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compute the remaining life of the initial transformer installations and the ones existing at the end of study period, respectively.
PWCSal =
T
⎡
⎣PWt ·
M
t=2
btj · Cj,ini · 1 − TLOLj,ini
110 kV
⎤
Neighboring substation connection
⎦
j= 1
j=2
j=1
+ PWT ·
M
Cj · 1 − TLOLj
20 kV
(23)
j=1
TLOLj,ini =
T
jt
·
t=1
TLOLj,rep =
N
DR Enabled Load
fbi,j · LOLtj,ini
Fig. 2. Test system showing the location of transformers in the substation.
(24) • Following constraint prevents the value of age of transformers from becoming negative due to maintenance actions.
i=1
N T
t i,j · LOLtj,rep
(25)
t=2 i=1
(26)
t+1 t −ˇi,j + ˇi,j ≤ 0 ∀t = 2, . . ., T − 1; j, i
(27)
t − ˇi,j
t t i,j = 1 − ˇi,j
∀t, j, i
(32)
4. Test system
t−1 + ˇi,j ≤ 0 ∀t = 2, . . ., T ; j, i
bti,j
Atj ≥ 0 ∀j, t
(28)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. M, N, and T denote total number of transformer locations, size choices, and number of year t , of planning, respectively. fbi,j is primary decision variable. btj , jt , ˇi,j t are intermediate binary variables. C and i,j j,ini and Cj represent the investment cost of the initially selected transformer and the one existing at the end of the planning period at location j, respectively. The numerical values of these intermediate variables are found by using (6)–(8). TLOLj,ini , TLOLj,rep , and TLOLj are the total accumulated loss-of-life over entire planning duration of transformer installations selected as initial, replacement, and the ones existing at the end of the study period. LOLtj,ini and LOLtj,rep are loss-of-life of initial and replacement transformer at year t, respectively. These LOL values are determined by Clause 5 and 7 techniques of [30]. t and t ) are deterThe values of intermediate binary variables (ˇi,j i,j mined by (26)–(28) that is subsequently used in LOL calculation. PWCSal is salvage value all the transformers. In order to retain the optimization problem to MIQP, the nonlinearity of exponential function (21) is removed by piecewise linear approximation. And, higher order nonlinearity due to products of binary variables in (22) and salvage value calculations are removed by introducing intermediate variables [29].
A typical Finnish urban primary distribution substation (110 kV/20 kV), as displayed in Fig. 2, is assumed as the test system. The substation area consists of residential and commercial customers. The substation comprises of two transformer locations. The transformers installed on these sites act as backup to each other during contingencies. The present peak load at the substation is 14 MVA. The load levels, their probability, and conforming energy prices for losses cost calculations are listed in Table 2. The average penalty of LC for critical load and cost of load shifting under DR are considered to be 15 D /kW h [31] and 0.20 D /kW h, respectively. DR capacity of commercial load is assumed to be equal to district heated residential load [32]. Load transfer capability to NSS during contingencies is assumed to be 6 MW. The switching time to NSS is considered to be 3 h for manual transfer and 1 h for remotely operated transfer. These switching time values are based on the current experience in distribution networks of Helsinki. The input data for transformer choices is given in Table 3. The transformers of similar thermal design are considered. Hottest-spot rise over ambient temperature, top-oil rise, oil time constant, winding time constant, and cooling mode are 80 ◦ C, 45 ◦ C, 75 min, 5 min, and oil natural air forced, respectively. Planning period is considered to be 40 years. During the whole planning period, load growth and discount rate values are set equal to 2.6% and 5%, respectively. Hourly electricity price data for Finland of year 2011 [33] is used in Table 2 Load levels and corresponding energy price.
3.2. Constraints of the objective function
Sr. no.
Load level (p.u.)
Probability
Energy price (D /MW h)
In addition to (9)–(11), (14)–(20), (26)–(28), and expressions for eliminating nonlinearities of higher than quadratic level, the optimization model comprises of the following constraints.
1 2 3 4 5
1 0.9 0.8 0.7 0.6
0.0075 0.0218 0.0796 0.0900 0.8011
100 89 80 68 46
• Only one transformer can be installed at each location j in the substation (29).
N
fbi,j ≤ 1 ∀j = 1, . . ., M
(29)
Table 3 Parameters of candidate transformers. Parameter
Transformer #1 (T1)
Transformer #2 (T2)
Transformer #3 (T3)
Nameplate ratings (MVA) Investment cost (kD ) Maintenance cost (kD ) No-load loss (kW) Load loss eq. resistance () Emergency ratings (%)
10 247 49 14.80 1.66 120
16 339 68 21.92 0.939 120
20 355 71 25.20 0.673 120
i=1
• The total LOL of a transformer cannot be more than 100% (1 p.u.). TLOLj,ini ≤ 1 ∀j = 1, . . ., M
(30)
TLOLj,rep ≤ 1 ∀j = 1, . . ., M
(31)
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transformers losses cost calculations. The average repair or replacement time is considered to be 120 h.
Table 4 Results of Case 1 obtained from proposed optimization model. Variables
Transformer location
5. Case studies’ results and discussions To demonstrate the use of the proposed model in quantification of the DR and network automation benefits for substation transformers capacity planning, results for the following case studies are presented. Case 1. Transformers at both locations in the substation are old. Also, ratings of in-service and replacement transformers are known. This case represents the usual situation faced by utilities in which replacement and/or refurbishment years of transformers are to be determined while other equipment in the substation limit the rating of new transformer installations. Here, it is assumed that load transfer to NSS during contingencies is accomplished by manual switches. Case 2. All the conditions are same as that of Case 1 except that the load transfer to NSS is performed by remote controlled switches. Case 3. In this case, transformers are optimally selected from available candidates for initial and subsequent installations in the planning period. This condition designates the situation of a new substation planning in which variety of transformer sizes are available and other equipment ratings will be decided based on the transformer selections. Here, it is assumed that the load transfer to NSS during contingencies is accomplished by manual switches. Case 4. All the conditions are the same as Case 3 except that the load transfer to NSS is performed via remote controlled switches. In addition to the above described cases, a sensitivity analysis is also performed for the following scenarios to investigate the impact of penetration of DR technology and penalty of LC on the results of the case studies. - Scenario 1: It is the base scenario whose results are computed by using input data presented in Section 4 and considering 100% DR penetration (all the flexible customers are responsive). - Scenario 2: In this scenario, DR penetration is assumed to be 50% (only 50% of the flexible customers are responsive). - Scenario 3: Load is considered unresponsive in this scenario. It provides the base for comparison of DR benefit. - Scenario 4: The reduced penalty of LC (7.5 D /kW h) is assumed in this scenario. - Scenario 5: This scenario assumes penalty of LC double (30 D /kW h) as compared to the base scenario. The MIQP problem formulated in Section 3 is solved via the general algebraic modelling system (GAMS) [34] environment, on 3.47 GHz, 24 GB, i7 computer station.
Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
824.8 278.7 582.6 – 70.3 106.8 17 –
829.8 294.7 572.9 – 74.8 112.6 15 –
1654.6 573.4 1155.5 – 145.1 219.4 17/15 –/–
Table 5 Sensitivity analysis results for Case 1. Scenario
S# 1-1: Base scenario S# 1-2: 50% DR penetration S# 1-3: No DR S# 1-4: Decreased LC penalty S# 1-5: Increased LC penalty
Replacement stage (yr)
Maintenance stage (yr)
j1
j2
j1
j2
17 17 16 17 17
15 15 13 15 12
– – 34 – 33
– – – – 33
by initial and replacement transformers during normal conditions on location j1 are 1.08 p.u. and 1.19 p.u. The total net present worth of costs is D 1654.6 k, out of which the shares of investment minus salvage, loss, maintenance, and interruption costs are about 21%, 70%, 0%, and 9%, respectively. Though the failure rate of initial transformer is high (0.0235 occurrences per annum at first year), yet refurbishment is not executed on them because combination of small probability of transformer failure at peak load and activation of DR keeps the interruption cost to a low level. The capacity deficits during peak load transformer failure at year 14 before and after load transfer to NSS with manual switches are of 7.5 MW and 1.5 MW, respectively. For a contingency at this point, the LC and DR activation requirements to keep the load within transformer limits are 16 MW h and 25 MW h, respectively. The interruption cost weighted by probability of failure (failure rate × peak hours = 0.00029) at this peak load is D 72 which is very low. The low interruption cost relative to the total cost is due to activation of DR. The low interruption cost also avoids the refurbishments of replacement transformers, although capacity deficit for peak load contingency at stage (yr) 39 is significant (18 MW). The results of sensitivity analysis are given in Table 5 and Fig. 3. In scenarios of 50% DR penetration (S#1-2), the replacement and refurbishment schedule does not change. However, increase in interruption cost is due to higher requirement of LC due to lesser DR capability. Absence of DR in S#1-3, prepones the replacement of transformers (to years 16 and 13) and requires refurbishment of
5.1. Case 1: old initial transformers and manual switching In this case, it is assumed that the existing transformers (10 MVA each) at both transformer locations (j1 and j2) in the substation are 20 years old with an estimated residual life of 50%. A replacement transformer of rating 16 MVA is to be mounted at each location in the planning horizon. The optimum time of transformer replacements, maintenance years, and transformers’ associated costs determined by the model presented in Section 3 are given in Table 4. It is assumed that all the flexible customers are responsive (100% DR penetration) and switching of load transfer to NSS is manual. The optimal stages of replacing old transformers are years 17 and 15 for locations j1 and j2, respectively. The peak loads observed
Total
Fig. 3. Sensitivity analysis results for Case 1.
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185 Table 6 Results of Case 2 obtained from proposed optimization model. Variables
Table 7 Sensitivity analysis results for Case 2.
Transformer location
Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
810.9 271.3 587.6 – 56.1 104.1 18 –
811.8 278.7 582.6 – 57.3 106.8 17 –
183
Scenario
Total
1622.7 550 1170.2 – 113.4 210.9 18/17 –/–
S# 2-1 S# 2-2 S# 2-3 S# 2-4 S# 2-5
Replacement stage (yr)
Maintenance stage (yr)
j1
j2
j1
j2
18 17 17 17 18
17 16 15 17 17
– – – – 34
– – – – 34
transformer of j1 at year 34 for the optimum solution. In this scenario, the total cost is higher compared to DR scenarios. If the LC penalty is halved (S#1-4) then total cost reduces due to decrease in interruption cost, however, replacement schedules remain same as of S#1-1. For the scenario of increased LC penalty (S#1-5), one of the transformer replacement is preponed (from year 15 to 12 at j2) and both replacement transformers need refurbishment (at year 33) to give optimal cost solution by maintaining the interruption cost at an acceptable level. Fig. 4. Sensitivity analysis results for Case 2.
5.2. Case 2: old initial transformers and remote switching In this case, it is assumed that all the conditions are same as of Case 1 except that the load transfer to NSS is performed by remote controlled switches. Table 6 lists the results for this case. The total net present worth of costs is D 1622.7 k, out of which the portions of investment cost minus salvage, loss cost, maintenance cost, and interruption cost are 21%, 72%, 0%, and 7%, respectively. Because of the shorter time for load transfer to NSS, the interruption cost share is a bit lower than that of Case 1. Therefore in optimum solution, the replacement of transformers is a bit delayed (for j1 from year 17 to 18 and for j2 from year 15 to 17) as compared to Case 1. For a peak load contingency at year 14, DR and LC requirements are 4 MW and 36 MW, respectively. Probable interruption cost (probability of transformer failure is 0.00029) at this point is D 18 which is relatively lesser than of Case 1. The losses cost of Case 2 is bit higher than that of Case 1 because lower rating initial transformer remains in service for longer duration in Case 2. The trend in sensitivity analysis results of Case 2, presented in Table 7 and Fig. 4, is similar to that of Case 1. For reduced DR penetration (S#2-2 and S#2-3), one of the transformer replacement is preponed and overall cost is higher due to increased interruption cost. The total cost is the lowest in S#2-4 due to least LC penalty. In scenario of increased LC penalty (S#2-5), replacement schedule is same as of S#2-1, however, transformer refurbishments are also required to decrease the interruption cost near end years. 5.3. Case 3: optimal selection and manual switching The optimum size selection of initial and replacement transformers for both the sites (j1 and j2) from available contenders are
Table 8 Results of Case 3 obtained from proposed optimization model. Variables
Transformer location
Rating of initial transformer (MVA) Rating of replacement transformer (MVA) Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
Total
(j1)
(j2)
10 20 762.6 525 470 – 13.5 245.9 6 –
10 20 762.6 525 470 – 13.5 245.9 6 –
10/10 20/20 1525.2 1050 940 – 27 491.8 6/6 –/–
acquired in this case. Load transfer to NSS is assumed via manual switches and full DR penetration is considered. The choices of transformer sizes, their replacement times, maintenance years, and associated costs determined by the model presented in Section 3 are listed in Table 8. It is cost-effective to mount 10 MVA transformers at both the locations in the beginning and replace them with 20 MVA transformers at year 6. Both the transformers at each location constitute equal share in the total net cost. Fractions of the costs of investment (minus salvage value), losses, maintenance, and interruption in the total net cost (D 1525.2 k) of this case are 36%, 62%, 0%, and 2%, respectively. Transformers’ size and replacement schedule is such that the total interruption cost is very low (D 27 k) with
Table 9 Sensitivity analysis results for Case 3. Scenario
S# 3-1 S# 3-2 S# 3-3 S# 3-4 S# 3-5
Replacement stage (yr)
Maintenance stage (yr)
Initial transformer (MVA)
Replacement transformer (MVA)
j1
j2
j1
j2
j1
j2
j1
j2
6 29 13 5 7
6 2 13 5 7
– – 11 – –
– – 11 – –
10 20 20 10 20
10 20 20 10 20
20 20 20 20 20
20 20 20 20 20
184
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
Fig. 5. Sensitivity analysis results for Case 3. Fig. 6. Sensitivity analysis results for Case 4. Table 10 Results of Case 4 obtained from proposed optimization model. Variables
Transformer location
Rating of initial transformer (MVA) Rating of replacement transformer (MVA) Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
10 20 758.8 525 470 – 9.7 245.9 6 –
10 20 758.8 525 470 – 9.7 245.9 6 –
Table 12 DR benefit comparison for case studies.
Total
Case
10/10 20/20 1517.6 1050 940 – 19.4 491.8 6/6 –/–
Total cost (kD )
Case 1 Case 2 Case 3 Case 4
the activation of DR. The normal peak loads observed by initial and replacement transformers do not increase to very high values (0.78 p.u. for 10 MVA transformers and 0.95 p.u. for 20 MVA transformers). The results of the sensitivity analysis are presented in Table 9 and Fig. 5. In scenarios of decreased DR penetration and increased LC penalty (S#3-2, S#3-3, and S#3-5), it is beneficial to use higher rating transformers (20 MVA) even as initial installations to obtain optimal total cost. In these scenarios, bigger transformer size selection enables the delay of replacement of transformers. Here, overall cost is higher than that of base scenario. For scenario of without DR (S#3-3), refurbishments of transformers are also required at year 11 to decrease interruption cost. Transformer size selection is same in decreased LC penalty scenario (S#3-4); however, replacements are preponed by one year for optimal solution. 5.4. Case 4: optimal selection and remote switching In this case, the only difference compared to Case 3 is that the remote switching for transferring load to NSS is used instead of manual switching. The results of the study are presented in Table 10. Optimal transformer sizes and their replacement schedule are same as of Case 3; however, slight decrease in total cost is
DR benefit
Scenario 1: 100% DR
Scenario 3: No DR
(kD )
1654.6 1622.7 1525.2 1517.6
1693.2 1663.2 1623.8 1618.9
38.6 40.5 98.6 101.3
due to reduction in interruption cost because fast transfer of load to NSS during contingencies that leads to a lesser interruption cost. In this case, the shares of cost of investment (minus salvage value), losses, maintenance, and interruption in the total net cost of this case are 37%, 62%, 0%, and 1%, respectively. Table 11 and Fig. 6 display the sensitivity analysis results. Transformer size selections for all the scenarios in this case are same as of Case 3. However, slight delay in replacement of transformers in S#4-2 and S#4-5 is due to short load transfer switching times that result into lower interruption costs. The comparison of total cost between Scenarios 1 and 3 provides the benefit of DR in transformer capacity planning. This comparison for all four cases is summarized in Table 12. The benefits of DR for Case 1, Case 2, Case 3 and Case 4 are D 38.6 k, D 40.5 k, D 98.6 k, and D 101.3 k, respectively. The DR benefit is relatively higher for cases in which load to NSS is transferred via remote switching than the cases of manual transfer. This difference in benefit based on type of switches would be greater for systems in which manual transfer takes longer times. The major reduction of load using DR is needed immediately following a contingency while load transfer to NSS is being arranged. DR is required for short time in Case 2 and Case 4 because of remote switching, so, higher decrease in load can be gained. Whereas in Case 1 and Case 3, DR is required for longer time due to manual switching. The load payback phenomenon decreases the load reduction capability in these cases. Therefore, the activation of DR is relatively more beneficial for cases of load transfer to NSS through remote switches.
Table 11 Sensitivity analysis results for Case 4. Scenario
S# 4-1 S# 4-2 S# 4-3 S# 4-4 S# 4-5
Replacement stage (yr)
Maintenance stage (yr)
Initial transformer (MVA)
Replacement transformer (MVA)
j1
j2
j1
j2
j1
j2
j1
j2
6 35 13 5 8
6 2 13 5 8
– – 11 – –
– – 11 – –
10 20 20 10 20
10 20 20 10 20
20 20 20 20 20
20 20 20 20 20
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
6. Conclusion This paper has proposed a novel optimization model for quantification of the savings in capacity management of substation transformers by incorporating the DR as a resource to reduce the outage cost during contingencies. The model also incorporates the impact of existing switching types for load transfer between substations. In the model, the decisions of optimum size selection and planning of multistage transformer installations and overhauls were attained by considering all the associated costs (i.e., investment, losses, maintenance, reliability, and salvage value). Simulations were performed for various case studies representing the situations faced by utilities and based on the type of load transfer switches for a typical Finnish primary distribution substation. Moreover, a sensitivity analysis was also conducted based on DR penetration and LC penalty value. The investigation of results indicated that significant monetary saving can be gained by employing DR in substation transformers planning. These savings are higher for systems in which load transfer to NSS is conducted by remotely operated switches. The proposed optimization model is valid for all load types (such as residential, commercial, and industrial). For various load types, difference would be only in input parameter values and correspondingly output results would be different. The proposed model in this article was useful in optimal capacity planning of transformers with DR. The DR also offers others benefits to power systems players. Further research is required for optimum division of DR for its various benefits. Moreover, realization of these benefits (including one proposed in this paper) are interesting research directions. Acknowledgements The first author of this paper would like to acknowledge that this work is funded by the Aalto energy efficiency program through the SAGA project. References [1] M. Humayun, M.Z. Degefa, A. Safdarian, M. Lehtonen, Utilization improvement of transformers using demand response, IEEE Trans. Power Delivery 30 (Feb. (1)) (2015) 202–210. [2] M. Humayun, B.J.O. Sousa, M.Z. Degefa, S. Kazemi, M. Lehtonen, Markov model based assessment for redundancy mitigation in high voltage grids using demand response, Int. Rev. Electr. Eng. 8 (Jul.–Aug. (4)) (2013) 1349–1362. [3] M. Humayun, A. Safdarian, M.Z. Degefa, M. Lehtonen, Demand response for operational life extension and efficient capacity utilization of power transformers during contingencies, IEEE Trans. Power Syst. 30 (Jul. (4)) (2015) 2160–2169. [4] M. Humayun, M. Ali, A. Safdarian, M.Z. Degefa, M. Lehtonen, Optimal use of demand response for lifesaving and efficient capacity utilization of power transformers during contingencies, in: Proc. 2015 IEE PES General Meeting, Jul. 26–30, 2015, Denver, CO, USA, 2015. [5] H.L. Willis, Power Distribution Planning Reference Book, CRC Press, New York, 2010. [6] S. Heidari, M. Fotuhi-Firuzabad, S. Kazemi, Power distribution network expansion planning considering distribution automation, IEEE Trans. Power Syst. 30 (May (3)) (2015) 1261–1269. [7] O. Siirto, A. Safdarian, M. Lehtonen, M. Fotuhi-Firuzabad, Optimal distribution network automation considering earth fault events, IEEE Trans. Smart Grid 6 (Mar. (2)) (2015) 1010–1018. [8] EC Directive 2009/72/EC, EC Directive 2009/72/EC of the European Parliament and of the Council of 13 July 2009, concerning common rules for the internal market in electricity and repealing Directive 2003/54/EC, Off. J.Eur. Union L211 (Aug.) (2009).
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(Online).
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Optimal capacity planning of substation transformers by demand response combined with network automation Muhammad Humayun a,∗ , Amir Safdarian b , Mubbashir Ali a , Merkebu Z. Degefa a , Matti Lehtonen a a b
Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland Department of Electrical Engineering, Center of Excellence in Power System Control and Management, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 13 August 2015 Received in revised form 10 January 2016 Accepted 13 January 2016 Keywords: Automation Planning Demand response Substation Transformer
a b s t r a c t The inclusion of smart grid features such as demand response (DR) and network automation for capacity planning of substation transformers may provide substantial monetary savings. This paper proposes an optimization model for quantification of the savings in capacity management of substation transformers over long-run. The proposed model incorporates the DR as a resource to decrease the outage cost during contingencies while considering existing switching types for load transfer between substations. The model provides optimal selection and scheduling of multistage transformer installations and their refurbishments by considering all the costs associated with them including investment, losses, maintenance, reliability, and the salvage value. For a realistic study, numerical value of the savings in transformers’ cost is calculated for a typical Finnish two-transformer primary distribution substation planning over a period of forty years. Case studies are performed based on situations encountered by utilities and type of load transfer switching (manual and remote) between substations. A sensitivity analysis based on DR penetration and load curtailment (LC) cost is also performed. The results indicate that substantial monetary benefits can be obtained in substation transformers’ cost by utilities through employing DR. The benefit of DR is superior for cases where it is used in combination with remote switching of load transfer between neighbouring substations (NSS). © 2016 Elsevier B.V. All rights reserved.
1. Introduction Smart grid features offer new opportunities for improving practices of the asset management in the future power systems. Demand response (DR) and network automation are the most critical features among others as they have impact on the load profile at feeders and transformers. Substation transformers, the most costly components in a distribution system, can gain substantial increase in their utilization efficiency by using these techniques [1–7]. These utilization gains may be obtained by activating DR and/or transferring load to neighbouring substations (NSS) following a contingency, thus releasing the reserve capacity for normal operation usage [2–7]. This reserve capacity is kept, due to conventional design requirements (e.g., N − 1), to provide support during contingencies which are rare events. The best time to consider DR for substation transformer capacity management is at the planning phase as extra investments in the
∗ Corresponding author. Tel.: +358 50 415 4331. E-mail address: muhammad.humayun@aalto.fi (M. Humayun). http://dx.doi.org/10.1016/j.epsr.2016.01.011 0378-7796/© 2016 Elsevier B.V. All rights reserved.
assets may be avoided resulting into higher utilization efficiency over their entire lifetime. This can be confirmed by the European Directive 2009/72/EC [8] emphasizing that the DR should be considered during planning stage of the distribution system capacity. The existing load transferring switch types (e.g., manual and remote) can have a significant impact on DR based planning solution [5–7]. This is because the DR cannot provide load reduction for longer time as flexible appliances cannot be turned off for many hours [9] and after certain time DR payback/rebound load also appears in the load profile. Therefore, activating DR potentials and the existing switching type for load transfer to NSS should be considered in parallel in the planning. In the literature of substation transformer capacity planning, the possible impact of employing DR in the planning process of distribution networks has not been well examined. The research in this field has almost been limited to the effect of DR in operational planning of distribution system and transformer capacity [1–4], [10–12]. The authors evaluated the utilization efficiency improvement of substation transformers using DR in [1–4]. The impact of electric vehicle load on the secondary distribution transformers and their integration using DR was evaluated in [13–15]. The
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
Nomenclature Sets and indices h, z, indices of hour in a year z , z index for choices of transformer sizes i j, j indices for transformer locations in a substation t, t indices of year index for load level of demand LL LLm number of load levels M number of transformer locations N number of transformer size choices number of years of planning T Parameters cDR unit incentive paid to customers for using their DR flexibility cLC unit load curtailment cost discount rate (based on inflation and interest rates) d hsw switch time, its value depends upon the type of load transfer (i.e., manual or remote) between substations loss equivalent resistance of transformer on location rjt j at year t y decrease in equivalent age of a transformer due to a maintenance action Ci procurement cost of transformer size i DLL duration of load level LL emergency rating multiplier of a transformer ER NLtj no-load loss of transformer on location j at year t NSSt PCt,z t,z PDR
t,z,z PDR t PEng,LL PWt max TDR Tr i
t i,j
jt , jt jt
DRz,z j,t,h
load deferred from hour z to later hour z
DRj,t,h
load deferred to z in prior hours z
LCzj,t,h
current flowing through transformer at location j, load level LL, and year t amount of critical load curtailed
z ,z
t Ij,LL
LOLtj,ini
LOLtj,rep NLtj z Pj,t,h PWC PWCtInt PWCtInv PWCtLoss PWCtMai PWCSal TECtj TLOLj
available flexible load at year t, hour z
TLOLj,ini
peak bound of variable for load deferred from hour z to later hour z energy price at load level LL and year t present worth factor of costs at year t maximum time for which a load can be deferred repair time of a transformer general symbol for parameters (of capacity, cost, resistance, and no-load of loss of transformer) of size i
dependent variables; unity value indicates that replacement transformer are in service dependent variables dependent variables; unity value indicates that initial transformer are in service decision for refurbishment of transformer at location j and year t
Continuous variables maintenance cost of transformer at location j and mctj year t age of transformer at location j and year t Atj ini CInv rep CInv
Capj ,ini Capj ,rep DRzj,t,h
investment cost of the transformer at j investment cost of initially selected transformer at location j capacity of initial transformer at location j capacity of replacement transformer at location j demand deferred under demand response
neighbouring substation capacity at year t available critical load at year t, hour z
Binary variables bti,j decision for selection of a transformer size as a replacement fbi,j decision for selection of a particular transformer i as initial transformer at location j t ˇi,j dependent variables ˇjt , ˇjt
Cj Cj,ini
investment cost of initial transformer investment cost of replacement transformer
177
TLOLj,rep j,ini
j,rep
tj
loss-of-life of initial transformer at location j and year t loss-of-life of replacement transformer at location j and year t no-load loss of transformer on location j at year t modified load profile after overload relieving actions total present value of costs of transformers in a substation present value of interruption/reliability cost at year t present worth of the investment cost at year t present worth of losses cost at year t present worth of maintenance cost at year t. present worth of salvage value of investments emergency capacity of healthy transformers during contingency of transformer at location j and year t total accumulated loss-of-life of transformer existing at j by the end of the study period total accumulated loss-of-life of initial transformer at location j total accumulated loss-of-life of replacement transformer at location j parametric values (capacity, cost, resistance, and no-load of loss) for initial transformers at location j parametric values (capacity, cost, resistance, and no-load of loss) for replacement transformers at location j failure rate of transformer at location j and year t
benefit of DR for reliability improvement of distribution systems was assessed in [11,12], [16,17]. The impact of DR and automation on distribution system reliability cost was discussed in [18]. Studies [19,20] reported that overinvestments in transmission network capacity can be avoided using DR at the planning stage. In [21], the substation capacity planning was in conjunction with distribution system reinforcement in presence of DR, however, transformer maintenance scheduling, increasing failure rate with aging, salvage value based on insulation loss-of-life (LOL), and load transfer to neighbouring substation (NSS) during contingencies were not incorporated. The authors also presented an optimization model [22] for substation capacity planning, but NSS support and DR features were not considered. Therefore, an appropriate tool for quantification of DR benefits considering load transferring switch types in substation capacity planning is needed. In this article, the influence of DR along with type of switches for load transferring to NSS is investigated on the optimal capacity planning of transformers for a primary substation. The impacts of DR and load transferring time to NSS are appropriately included in outage cost calculation of the proposed optimization model for
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planning and management of transformer capacities in a substation. The optimization model accounts all the costs related with the transformers including investment cost, operational cost, reliability cost, and salvage value. In the optimization model, transformer increase in failure rate with age and salvage value based on the insulation LOL are also incorporated. The model decides the optimal selection of transformers’ sizes, their maintenance times, and stage of transformers replacements in the planning horizon in order to reduce the present worth of total cost to satisfy the given load. A simulation is developed to quantify the benefits of DR while considering load transfer switching times. Using the simulation, numerical results are obtained and analysed for capacity planning of a typical Finnish two-transformer primary distribution substation. Demand profile and DR capacity of the load are estimated by hourly measured consumption and survey data from central Finland. Case studies are performed based on situations encountered by utilities and load transfer switching types (i.e., manual and remote). A broad sensitivity analysis is also performed considering the variation in DR penetration of load and load curtailment (LC) cost. Numerical results indicate that the utilization of DR can provide substantial saving in total substation transformer costs. The savings are superior when combination of DR and remote switching are applied instead of DR with manual load transfer switching. This paper is organized as follows: Section 2 provides the DR capability related information. The optimization model is formulated in Section 3. The test system details are provided in Section 4. Section 5 describes the case studies’ results and discussion. The conclusions follow in Section 6. 2. Demand response capability This section provides the DR basics, DR potential of household appliances, and the method of determining DR capability of the load profile at the primary substation level. DR is defined as “changes in electricity usage by the end-use customers from their normal consumption pattern in response to changes in the price of electricity over time or when system reliability is jeopardized” [23]. Based on flexibility in operation, domestic electrical appliances are classified into two categories: controllable and critical. The operation of controllable appliances can be moved in time whereas critical appliances do not offer such flexibility in operation. It is worth mentioning that controllable loads are also referred to as responsive loads. Washing machines and dishwashers can offer flexibility in operation by delaying wash action and altering cycle duration. DR in clothes dryers can be realized by postponing its operation or by changing heating phase time. In cold appliances (refrigerator and freezer), DR can be achieved by deferring ice forming and defrost actions, modifying on-time cycle, and allowing slight temperature modifications during emergency
Table 1 Demand response potential of domestic appliances [25,26]. Appliance
DR potential (h)
Refrigerator/freezer/air conditioner/clothes dryer/direct space heating Storage water heater Washing machine Storage space heating/dish washer
1
3 4 5
periods. Similarly, heaters and air conditioners offer flexibility by rescheduling run time and altering temperature bounds within the limits set by users. The distinctive nature of heating loads, instigated by thermal inertia, makes them greatly responsive [24]. Table 1 lists the DR time shifting capacity of controllable appliances [25,26] considered in this article. Rest all the devices (television, personal computer, stove, lighting, etc.) are in the category of critical appliances. In order to determine the available DR capability of load at a particular time, along with flexibility of each appliance, the disaggregated load profile of controllable appliances is also needed. For that, a one year automatic meter reading hourly load data measured from 1600 residential consumers in central Finland is used to build the load profile of the transformers. Then, conditional demand analysis (a statistical regression technique) is applied to this metered data, weather information, and statistical data collected by survey [27] to achieve the demand disaggregation. The survey data contains the information related to houses, people living in them, and electrical appliances. The disaggregated load profile of a typical winter week-day for a typical house is shown in Fig. 1. Finally, average DR capability of demand is determined by using the disaggregated demand and DR values of appliances from Table 1, as obtained in [1,3]. 3. Problem formulation This section proposes a mixed integer quadratic programming (MIQP) optimization formulation for capacity management of substation transformers in presence of DR and NSS connection. Assume that a transformer can be installed on each transformer location at a substation from available choices in the beginning of planning phase. A new transformer from available choices can replace the current transformer at a later phase at each location. Furthermore, maintenance/refurbishment activities can be performed to decrease the failure probability of transformers. During the failure of transformers, load on healthy transformers can be reduced by activating DR, by transferring load to neighbouring substations (if there is free capacity), and/or by LC. The aim is to find a set of decision variables indicating transformers’ selection of ratings, stage
Fig. 1. Disaggregated load profile of a typical winter week–day for a typical house.
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
(year) of maintenance, and time of replacements in the planning horizon such that the total cost is minimized for the transformers. 3.1. Objective function The objective of optimization model is formulated as (1); the goal is to minimize total cost of transformers in a substation over the entire planning period. Minimize PWC =
T
PWCtInv + PWCtLoss + PWCtMai + PWCtInt
t=1
− PWCSal
(1)
where t and T are index of year and its maximum value, respectively. PWC is present worth of total cost of transformers in a substation. PWCtInv , PWCtLoss , PWCtMai , and PWCtInt are present worth of investments, losses, maintenance, and interruption/reliability costs at year t, respectively. PWCSal denotes the salvage value of investments. The details of each cost component are given in the following: (1) Investment cost: The investment cost of transformers depends on their ratings and internal design. In this paper, transformer costs of procurement, commission, and decommissioning are included in the investment cost. The investment cost of initial and replacement transformer installations is given by the following expressions. ini PWCtInv = CInv =
N M
Ci · fbi,j t = 1
(2)
j=1 i=1
rep
PWCtInv = CInv = PWt ·
N M
Ci · bti,j
∀t = 2, . . ., T
(3)
j=1 i=1
PWt =
1 (1 + d)
t−1
∀t
(4)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. Ci refers to the procurement cost of transformer size i. fbi,j and bti,j are binary decision variables denoting the selection of a particular size transformer at each location as initial and replacement installations, respectively. M and N denote total number of transformer location in the substation ini and C rep and number of transformer size choices, respectively. CInv Inv represent the cost of initial and replacement transformers, respectively. PWt is the present worth factor and d is the discount rate (based on inflation and interest rates). The investment cost at the beginning of planning horizon in (2) is sum of investment cost of first transformer installations at each location. The present worth of investment cost of replacement transformers in (3) depends on the size of replacements transformer and year of replacement. (2) Losses cost: Eq. (5) provides the yearly present worth cost of substation transformer losses. These losses cost depends upon the transformers’ winding loss, core loss, and energy price. PWCtLoss = PWt ·
M LLm j=1 LL=1
2
t ) · r t + NLt (Ij,LL j j
t ·DLL · PEng,LL
∀t
(5)
179
transformer which is calculated based on transformer rating, voltage, and load value. rjt and NLtj are transformer’s loss equivalent winding resistance and nominal no-load loss, respectively. DLL is t duration of a load level and PEng,LL is energy price. PWt and PWCtLoss represent the present worth factor and present worth of losses cost, respectively. As values of the transformer parameters (resistance and noload loss) depends upon the transformer selection made by the optimization model from various alternatives. Therefore, consistent values of these parameters should be considered in the calculation. These parametric values (resistance and no-load loss) of transformers required in (5) are calculated by the following equations:
j,ini =
N
i · fbi,j
(6)
i=1
j,rep =
N T
i · bti,j
(7)
t=2 i=1
tj = jt · j,ini + ˇjt · j,rep
∀t = 2, . . ., T
btj − ˇjt + ˇjt−1 = 0 ∀t = 2, . . ., T and btj =
(8) N
bti,j
(9)
i=1
−ˇjt+1 + ˇjt ≤ 0 ∀t = 2, . . ., T − 1
(10)
jt + ˇjt = 1 ∀t = 1, . . ., T
(11)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. N and T denote total number of transformer size choices and number of years of planning, respectively. fbi,j and bti,j are primary binary decision variables of transformer selection. , j , j,ini , and j,rep refer to the general symbol for transformer parameters (capacity, cost, resistance, and no-load loss), their value for initial, and replacement transformers, respectively. jt and ˇjt are dependent binary variables whose unity value indicates the initial and replacement installation of a transformer as in-service, respectively. Eqs. (6) and (7) are used to find the parametric values of initial and replacement transformers. The parameters of initial transformer selections are the values at the first year; however, either initial or replacement transformer can be present at later years. Therefore, (8)–(11) are utilized in order to determine the parameters of transformer installations for year 2 or later. Eqs. (9)–(11) guarantee that once an initial transformer is replaced by a new transformer at a location then unity value is allotted to ˇjt for all the future years. (3) Maintenance cost: Typically, the cost of maintenance inspections and actions is low; however, main refurbishments are of significant cost. In this manuscript, maintenance refers to these main refurbishment actions that decreases the failure probability of the transformers. The maintenance cost of transformers in a substation is determined by the following equation:
PWCtMai = PWt ·
M
jt · mctj
(12)
j=1
where j, LL, and t are the indices of transformer location, load level of demand, and planning year, respectively. M and LLm denote total number of transformer location in the substation and number of t denotes the current flowing through load levels, respectively. Ij,LL
where j and t are the indices of transformer location and planning year, respectively. M denotes the total number of transformer locations in the substation. jt is binary decision variable indicating
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an overhaul action at year t on location j. mctj is cost of maintenance whose value depends on the in-service transformer size which is determined by using (6)–(8). PWt and PWCtMai represent the present worth factor and present worth of maintenance cost, respectively. (4) Interruption/reliability cost: The present worth of yearly interruption cost of transformers is calculated by (13). It is determined by considering transformer failures while considering instance of failures, failure rates, load curtailed, and DR activated.
PWCtInt
t
= PW
8760 M
tj 8760
j=1 h=1
·
h+Tr
cLC · LCzj,t,h
+ cDR · DRzj,t,h
z=h
(13) where j, t, h, and z are the indices of transformer location, planning year, hour of a year, and hour of repair, respectively. M and Tr denote the total number of transformer locations in the substation and average repair time for transformers, respectively. LCzj,t,h and
DRzj,t,h are variables representing the amounts of load curtailed and demand deferred, respectively. cLC and cDR are unit cost of LC and DR, respectively. tj denotes the transformer failure rate per annum. In (13) at first, a transformer failure is assumed at an hour (h) in a year (t) for a particular transformer at location (j) in a substation. Then, outage cost is calculated for that contingency, which is the sum of load curtailment cost for critical load and load under DR during each hour of the repair duration. After that, this outage cost is multiplied by transformer failure probability at that hour in a year. Subsequently, outage cost of that transformer considering contingencies occurring at each hour of a year (8760 h) is summed. Similarly, outage costs of all the transformers at a substation are added. Finally, this summed outage cost is weighted by the present worth factor. As transformers loads are hourly varying and also DR potentials also are different at different hours, therefore, limiting substation load below their peak capacity require time varying optimal load alleviation decision. The decision variables of LC and DR activation are determined by the following equations:
∀z < h + hsw
z Pj,t,h ≤ TECtj
∀z ≥ h + hsw
z Pj,t,h ≤ TECtj +NSSt
(14) (15)
TECtj =
jt · Capj ,ini + ˇjt · Capj ,rep · ER
(16) Atj = jt ·
j =1,j = / j t,z z Pj,t,h = PDR + PCt,z +
z
,z DRzj,t,h − LCzj,t,h −
t,z 0 ≤ LCzj,t,h ≤ PDR + PCt,z +
DRz,z ≤ j,t,h
z
DRzj,t,h =
,z DRzj,t,h −
DRz,z j,t,h
(17)
DRz,z j,t,h
(18)
z
t,z,z max PDR ∀z < z andz ∈ z + 1, 2, . . ., TDR
(19)
z
max DRz,z ∀z < z andz ∈ z + 1, 2, . . ., TDR j,t,h
t t =1
z
z
,z max times z , and DRzj,t,h load deferred to hour z in prior times z . TDR is the maximum time for which a load can be deferred. Load at any time should not be greater than the sum of maximum allowed loading of the transformer. The constraints (14) and (15) bound the modified load profile after LC and DR activation within the defined capacity limits. During switching time (14), only available transformers’ capacity is emergency capacity of healthy transformers in the same substation because load transfer to neighbouring substations is being arranged. Whereas, NSS capacity is also available to support the load after switching times (15) as load transfer actions has already been conducted. Eq. (16) determines the emergency load carrying capacity of healthy transformers in the same substation which is the sum of capacity of healthy transformers multiplied by their emergency rating multipliers. The modified load profile during a contingency is determined by (17) which is the sum of available flexible load, critical load, load deferred in prior times minus load curtailed, and load deferred to later times. The third term on the right hand side of equality in (17) is for load recovery that was deferred in earlier hours. Eq. (18) defines the upper limit of LC that depends on flexible load, critical load, and prior and current DR decisions. The constraint (19) sets the limit of DR activation; the sum of load that can be postponed to a later time is limited to the sum of power available under DR contract. Eqs. (18) and (19) ensure that LC and DR do not cross their logical limits. Eq. (20) determines the total load deferred under DR at any time which is the sum of loads that are postponed to all possible future times. Utilities’ experience indicates that the failure rate of transformers increases with their age. Ref. [28] provides an exponential expression (21) for estimating the transformer increasing failure rate. The reasons of considering this growing rate of transformers in this model are to imitate real failure mechanism and significance of reliability/interruption cost in transformer replacement planning. The interruption cost directly depends on failure rate. Eq. (22) is used to calculate the age of transformers.
tj = f (Atj ) = 0.001 exp(0.0944 · Atj ) + 0.0169
M
and emergency load carrying capability of healthy transformers in a substation, respectively. ˇjt and jt are dependent binary variables. hsw is switching time of load to NSS whose value is selected based on the type of load transfer (i.e., manual or remote) between substations. Capj ,ini and Capj ,rep are capacity of initial and replacement transformers at location j , respectively. NSSt is NSS load receiving capability. LCzj,t,h is load curtailed, DRz,z is load deferred to later j,t,h
(20)
z
where z, z , and z are the indices of hour of year during transformer t,z z , PCt,z , and Pj,t,h are available flexible load, critical load, and repair. PDR modified load profile after LC and DR activation, respectively. ER and TECtj denote the emergency rating multiplier of transformers
jt − y · jt · jt
+ ˇjt ·
t
(21)
ˇjt − y · jt · ˇjt
(22)
t =1
where j is index of transformer location in the substation. t and t are indices of planning year. tj is failure rate of transformer, Atj denotes the number of years conceded since the transformer installation. ˇjt ,
ˇjt , jt and jt are dependent binary variables. jt and y are binary decision variable indicating an overhaul action at year t on location j and corresponding decrease in the age of transformer due to that maintenance action, respectively. The first summation term in (22) provides the value of Atj if the initial transformer installation is supplying the load, while the second summation term is utilized in case the replacement installation is in service during the present year. The second sub-term in each summation denotes the reduction in failure rate of transformers due to maintenance actions. (5) Salvage value: The salvage (residual) values of transformers at the end of planning period or at the time of retirement/replacement are calculated by (23)–(28). The first and second terms in (23)
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
181
compute the remaining life of the initial transformer installations and the ones existing at the end of study period, respectively.
PWCSal =
T
⎡
⎣PWt ·
M
t=2
btj · Cj,ini · 1 − TLOLj,ini
110 kV
⎤
Neighboring substation connection
⎦
j= 1
j=2
j=1
+ PWT ·
M
Cj · 1 − TLOLj
20 kV
(23)
j=1
TLOLj,ini =
T
jt
·
t=1
TLOLj,rep =
N
DR Enabled Load
fbi,j · LOLtj,ini
Fig. 2. Test system showing the location of transformers in the substation.
(24) • Following constraint prevents the value of age of transformers from becoming negative due to maintenance actions.
i=1
N T
t i,j · LOLtj,rep
(25)
t=2 i=1
(26)
t+1 t −ˇi,j + ˇi,j ≤ 0 ∀t = 2, . . ., T − 1; j, i
(27)
t − ˇi,j
t t i,j = 1 − ˇi,j
∀t, j, i
(32)
4. Test system
t−1 + ˇi,j ≤ 0 ∀t = 2, . . ., T ; j, i
bti,j
Atj ≥ 0 ∀j, t
(28)
where i, j, and t are the indices of transformer size, transformer location, and planning year, respectively. M, N, and T denote total number of transformer locations, size choices, and number of year t , of planning, respectively. fbi,j is primary decision variable. btj , jt , ˇi,j t are intermediate binary variables. C and i,j j,ini and Cj represent the investment cost of the initially selected transformer and the one existing at the end of the planning period at location j, respectively. The numerical values of these intermediate variables are found by using (6)–(8). TLOLj,ini , TLOLj,rep , and TLOLj are the total accumulated loss-of-life over entire planning duration of transformer installations selected as initial, replacement, and the ones existing at the end of the study period. LOLtj,ini and LOLtj,rep are loss-of-life of initial and replacement transformer at year t, respectively. These LOL values are determined by Clause 5 and 7 techniques of [30]. t and t ) are deterThe values of intermediate binary variables (ˇi,j i,j mined by (26)–(28) that is subsequently used in LOL calculation. PWCSal is salvage value all the transformers. In order to retain the optimization problem to MIQP, the nonlinearity of exponential function (21) is removed by piecewise linear approximation. And, higher order nonlinearity due to products of binary variables in (22) and salvage value calculations are removed by introducing intermediate variables [29].
A typical Finnish urban primary distribution substation (110 kV/20 kV), as displayed in Fig. 2, is assumed as the test system. The substation area consists of residential and commercial customers. The substation comprises of two transformer locations. The transformers installed on these sites act as backup to each other during contingencies. The present peak load at the substation is 14 MVA. The load levels, their probability, and conforming energy prices for losses cost calculations are listed in Table 2. The average penalty of LC for critical load and cost of load shifting under DR are considered to be 15 D /kW h [31] and 0.20 D /kW h, respectively. DR capacity of commercial load is assumed to be equal to district heated residential load [32]. Load transfer capability to NSS during contingencies is assumed to be 6 MW. The switching time to NSS is considered to be 3 h for manual transfer and 1 h for remotely operated transfer. These switching time values are based on the current experience in distribution networks of Helsinki. The input data for transformer choices is given in Table 3. The transformers of similar thermal design are considered. Hottest-spot rise over ambient temperature, top-oil rise, oil time constant, winding time constant, and cooling mode are 80 ◦ C, 45 ◦ C, 75 min, 5 min, and oil natural air forced, respectively. Planning period is considered to be 40 years. During the whole planning period, load growth and discount rate values are set equal to 2.6% and 5%, respectively. Hourly electricity price data for Finland of year 2011 [33] is used in Table 2 Load levels and corresponding energy price.
3.2. Constraints of the objective function
Sr. no.
Load level (p.u.)
Probability
Energy price (D /MW h)
In addition to (9)–(11), (14)–(20), (26)–(28), and expressions for eliminating nonlinearities of higher than quadratic level, the optimization model comprises of the following constraints.
1 2 3 4 5
1 0.9 0.8 0.7 0.6
0.0075 0.0218 0.0796 0.0900 0.8011
100 89 80 68 46
• Only one transformer can be installed at each location j in the substation (29).
N
fbi,j ≤ 1 ∀j = 1, . . ., M
(29)
Table 3 Parameters of candidate transformers. Parameter
Transformer #1 (T1)
Transformer #2 (T2)
Transformer #3 (T3)
Nameplate ratings (MVA) Investment cost (kD ) Maintenance cost (kD ) No-load loss (kW) Load loss eq. resistance () Emergency ratings (%)
10 247 49 14.80 1.66 120
16 339 68 21.92 0.939 120
20 355 71 25.20 0.673 120
i=1
• The total LOL of a transformer cannot be more than 100% (1 p.u.). TLOLj,ini ≤ 1 ∀j = 1, . . ., M
(30)
TLOLj,rep ≤ 1 ∀j = 1, . . ., M
(31)
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M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
transformers losses cost calculations. The average repair or replacement time is considered to be 120 h.
Table 4 Results of Case 1 obtained from proposed optimization model. Variables
Transformer location
5. Case studies’ results and discussions To demonstrate the use of the proposed model in quantification of the DR and network automation benefits for substation transformers capacity planning, results for the following case studies are presented. Case 1. Transformers at both locations in the substation are old. Also, ratings of in-service and replacement transformers are known. This case represents the usual situation faced by utilities in which replacement and/or refurbishment years of transformers are to be determined while other equipment in the substation limit the rating of new transformer installations. Here, it is assumed that load transfer to NSS during contingencies is accomplished by manual switches. Case 2. All the conditions are same as that of Case 1 except that the load transfer to NSS is performed by remote controlled switches. Case 3. In this case, transformers are optimally selected from available candidates for initial and subsequent installations in the planning period. This condition designates the situation of a new substation planning in which variety of transformer sizes are available and other equipment ratings will be decided based on the transformer selections. Here, it is assumed that the load transfer to NSS during contingencies is accomplished by manual switches. Case 4. All the conditions are the same as Case 3 except that the load transfer to NSS is performed via remote controlled switches. In addition to the above described cases, a sensitivity analysis is also performed for the following scenarios to investigate the impact of penetration of DR technology and penalty of LC on the results of the case studies. - Scenario 1: It is the base scenario whose results are computed by using input data presented in Section 4 and considering 100% DR penetration (all the flexible customers are responsive). - Scenario 2: In this scenario, DR penetration is assumed to be 50% (only 50% of the flexible customers are responsive). - Scenario 3: Load is considered unresponsive in this scenario. It provides the base for comparison of DR benefit. - Scenario 4: The reduced penalty of LC (7.5 D /kW h) is assumed in this scenario. - Scenario 5: This scenario assumes penalty of LC double (30 D /kW h) as compared to the base scenario. The MIQP problem formulated in Section 3 is solved via the general algebraic modelling system (GAMS) [34] environment, on 3.47 GHz, 24 GB, i7 computer station.
Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
824.8 278.7 582.6 – 70.3 106.8 17 –
829.8 294.7 572.9 – 74.8 112.6 15 –
1654.6 573.4 1155.5 – 145.1 219.4 17/15 –/–
Table 5 Sensitivity analysis results for Case 1. Scenario
S# 1-1: Base scenario S# 1-2: 50% DR penetration S# 1-3: No DR S# 1-4: Decreased LC penalty S# 1-5: Increased LC penalty
Replacement stage (yr)
Maintenance stage (yr)
j1
j2
j1
j2
17 17 16 17 17
15 15 13 15 12
– – 34 – 33
– – – – 33
by initial and replacement transformers during normal conditions on location j1 are 1.08 p.u. and 1.19 p.u. The total net present worth of costs is D 1654.6 k, out of which the shares of investment minus salvage, loss, maintenance, and interruption costs are about 21%, 70%, 0%, and 9%, respectively. Though the failure rate of initial transformer is high (0.0235 occurrences per annum at first year), yet refurbishment is not executed on them because combination of small probability of transformer failure at peak load and activation of DR keeps the interruption cost to a low level. The capacity deficits during peak load transformer failure at year 14 before and after load transfer to NSS with manual switches are of 7.5 MW and 1.5 MW, respectively. For a contingency at this point, the LC and DR activation requirements to keep the load within transformer limits are 16 MW h and 25 MW h, respectively. The interruption cost weighted by probability of failure (failure rate × peak hours = 0.00029) at this peak load is D 72 which is very low. The low interruption cost relative to the total cost is due to activation of DR. The low interruption cost also avoids the refurbishments of replacement transformers, although capacity deficit for peak load contingency at stage (yr) 39 is significant (18 MW). The results of sensitivity analysis are given in Table 5 and Fig. 3. In scenarios of 50% DR penetration (S#1-2), the replacement and refurbishment schedule does not change. However, increase in interruption cost is due to higher requirement of LC due to lesser DR capability. Absence of DR in S#1-3, prepones the replacement of transformers (to years 16 and 13) and requires refurbishment of
5.1. Case 1: old initial transformers and manual switching In this case, it is assumed that the existing transformers (10 MVA each) at both transformer locations (j1 and j2) in the substation are 20 years old with an estimated residual life of 50%. A replacement transformer of rating 16 MVA is to be mounted at each location in the planning horizon. The optimum time of transformer replacements, maintenance years, and transformers’ associated costs determined by the model presented in Section 3 are given in Table 4. It is assumed that all the flexible customers are responsive (100% DR penetration) and switching of load transfer to NSS is manual. The optimal stages of replacing old transformers are years 17 and 15 for locations j1 and j2, respectively. The peak loads observed
Total
Fig. 3. Sensitivity analysis results for Case 1.
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185 Table 6 Results of Case 2 obtained from proposed optimization model. Variables
Table 7 Sensitivity analysis results for Case 2.
Transformer location
Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
810.9 271.3 587.6 – 56.1 104.1 18 –
811.8 278.7 582.6 – 57.3 106.8 17 –
183
Scenario
Total
1622.7 550 1170.2 – 113.4 210.9 18/17 –/–
S# 2-1 S# 2-2 S# 2-3 S# 2-4 S# 2-5
Replacement stage (yr)
Maintenance stage (yr)
j1
j2
j1
j2
18 17 17 17 18
17 16 15 17 17
– – – – 34
– – – – 34
transformer of j1 at year 34 for the optimum solution. In this scenario, the total cost is higher compared to DR scenarios. If the LC penalty is halved (S#1-4) then total cost reduces due to decrease in interruption cost, however, replacement schedules remain same as of S#1-1. For the scenario of increased LC penalty (S#1-5), one of the transformer replacement is preponed (from year 15 to 12 at j2) and both replacement transformers need refurbishment (at year 33) to give optimal cost solution by maintaining the interruption cost at an acceptable level. Fig. 4. Sensitivity analysis results for Case 2.
5.2. Case 2: old initial transformers and remote switching In this case, it is assumed that all the conditions are same as of Case 1 except that the load transfer to NSS is performed by remote controlled switches. Table 6 lists the results for this case. The total net present worth of costs is D 1622.7 k, out of which the portions of investment cost minus salvage, loss cost, maintenance cost, and interruption cost are 21%, 72%, 0%, and 7%, respectively. Because of the shorter time for load transfer to NSS, the interruption cost share is a bit lower than that of Case 1. Therefore in optimum solution, the replacement of transformers is a bit delayed (for j1 from year 17 to 18 and for j2 from year 15 to 17) as compared to Case 1. For a peak load contingency at year 14, DR and LC requirements are 4 MW and 36 MW, respectively. Probable interruption cost (probability of transformer failure is 0.00029) at this point is D 18 which is relatively lesser than of Case 1. The losses cost of Case 2 is bit higher than that of Case 1 because lower rating initial transformer remains in service for longer duration in Case 2. The trend in sensitivity analysis results of Case 2, presented in Table 7 and Fig. 4, is similar to that of Case 1. For reduced DR penetration (S#2-2 and S#2-3), one of the transformer replacement is preponed and overall cost is higher due to increased interruption cost. The total cost is the lowest in S#2-4 due to least LC penalty. In scenario of increased LC penalty (S#2-5), replacement schedule is same as of S#2-1, however, transformer refurbishments are also required to decrease the interruption cost near end years. 5.3. Case 3: optimal selection and manual switching The optimum size selection of initial and replacement transformers for both the sites (j1 and j2) from available contenders are
Table 8 Results of Case 3 obtained from proposed optimization model. Variables
Transformer location
Rating of initial transformer (MVA) Rating of replacement transformer (MVA) Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
Total
(j1)
(j2)
10 20 762.6 525 470 – 13.5 245.9 6 –
10 20 762.6 525 470 – 13.5 245.9 6 –
10/10 20/20 1525.2 1050 940 – 27 491.8 6/6 –/–
acquired in this case. Load transfer to NSS is assumed via manual switches and full DR penetration is considered. The choices of transformer sizes, their replacement times, maintenance years, and associated costs determined by the model presented in Section 3 are listed in Table 8. It is cost-effective to mount 10 MVA transformers at both the locations in the beginning and replace them with 20 MVA transformers at year 6. Both the transformers at each location constitute equal share in the total net cost. Fractions of the costs of investment (minus salvage value), losses, maintenance, and interruption in the total net cost (D 1525.2 k) of this case are 36%, 62%, 0%, and 2%, respectively. Transformers’ size and replacement schedule is such that the total interruption cost is very low (D 27 k) with
Table 9 Sensitivity analysis results for Case 3. Scenario
S# 3-1 S# 3-2 S# 3-3 S# 3-4 S# 3-5
Replacement stage (yr)
Maintenance stage (yr)
Initial transformer (MVA)
Replacement transformer (MVA)
j1
j2
j1
j2
j1
j2
j1
j2
6 29 13 5 7
6 2 13 5 7
– – 11 – –
– – 11 – –
10 20 20 10 20
10 20 20 10 20
20 20 20 20 20
20 20 20 20 20
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Fig. 5. Sensitivity analysis results for Case 3. Fig. 6. Sensitivity analysis results for Case 4. Table 10 Results of Case 4 obtained from proposed optimization model. Variables
Transformer location
Rating of initial transformer (MVA) Rating of replacement transformer (MVA) Net cost (kD ) Investment cost (kD ) Loss cost (kD ) Maintenance cost (kD ) Interruption cost (kD ) Salvage value (kD ) Replacement stage (yr) Maintenance stage (yr)
(j1)
(j2)
10 20 758.8 525 470 – 9.7 245.9 6 –
10 20 758.8 525 470 – 9.7 245.9 6 –
Table 12 DR benefit comparison for case studies.
Total
Case
10/10 20/20 1517.6 1050 940 – 19.4 491.8 6/6 –/–
Total cost (kD )
Case 1 Case 2 Case 3 Case 4
the activation of DR. The normal peak loads observed by initial and replacement transformers do not increase to very high values (0.78 p.u. for 10 MVA transformers and 0.95 p.u. for 20 MVA transformers). The results of the sensitivity analysis are presented in Table 9 and Fig. 5. In scenarios of decreased DR penetration and increased LC penalty (S#3-2, S#3-3, and S#3-5), it is beneficial to use higher rating transformers (20 MVA) even as initial installations to obtain optimal total cost. In these scenarios, bigger transformer size selection enables the delay of replacement of transformers. Here, overall cost is higher than that of base scenario. For scenario of without DR (S#3-3), refurbishments of transformers are also required at year 11 to decrease interruption cost. Transformer size selection is same in decreased LC penalty scenario (S#3-4); however, replacements are preponed by one year for optimal solution. 5.4. Case 4: optimal selection and remote switching In this case, the only difference compared to Case 3 is that the remote switching for transferring load to NSS is used instead of manual switching. The results of the study are presented in Table 10. Optimal transformer sizes and their replacement schedule are same as of Case 3; however, slight decrease in total cost is
DR benefit
Scenario 1: 100% DR
Scenario 3: No DR
(kD )
1654.6 1622.7 1525.2 1517.6
1693.2 1663.2 1623.8 1618.9
38.6 40.5 98.6 101.3
due to reduction in interruption cost because fast transfer of load to NSS during contingencies that leads to a lesser interruption cost. In this case, the shares of cost of investment (minus salvage value), losses, maintenance, and interruption in the total net cost of this case are 37%, 62%, 0%, and 1%, respectively. Table 11 and Fig. 6 display the sensitivity analysis results. Transformer size selections for all the scenarios in this case are same as of Case 3. However, slight delay in replacement of transformers in S#4-2 and S#4-5 is due to short load transfer switching times that result into lower interruption costs. The comparison of total cost between Scenarios 1 and 3 provides the benefit of DR in transformer capacity planning. This comparison for all four cases is summarized in Table 12. The benefits of DR for Case 1, Case 2, Case 3 and Case 4 are D 38.6 k, D 40.5 k, D 98.6 k, and D 101.3 k, respectively. The DR benefit is relatively higher for cases in which load to NSS is transferred via remote switching than the cases of manual transfer. This difference in benefit based on type of switches would be greater for systems in which manual transfer takes longer times. The major reduction of load using DR is needed immediately following a contingency while load transfer to NSS is being arranged. DR is required for short time in Case 2 and Case 4 because of remote switching, so, higher decrease in load can be gained. Whereas in Case 1 and Case 3, DR is required for longer time due to manual switching. The load payback phenomenon decreases the load reduction capability in these cases. Therefore, the activation of DR is relatively more beneficial for cases of load transfer to NSS through remote switches.
Table 11 Sensitivity analysis results for Case 4. Scenario
S# 4-1 S# 4-2 S# 4-3 S# 4-4 S# 4-5
Replacement stage (yr)
Maintenance stage (yr)
Initial transformer (MVA)
Replacement transformer (MVA)
j1
j2
j1
j2
j1
j2
j1
j2
6 35 13 5 8
6 2 13 5 8
– – 11 – –
– – 11 – –
10 20 20 10 20
10 20 20 10 20
20 20 20 20 20
20 20 20 20 20
M. Humayun et al. / Electric Power Systems Research 134 (2016) 176–185
6. Conclusion This paper has proposed a novel optimization model for quantification of the savings in capacity management of substation transformers by incorporating the DR as a resource to reduce the outage cost during contingencies. The model also incorporates the impact of existing switching types for load transfer between substations. In the model, the decisions of optimum size selection and planning of multistage transformer installations and overhauls were attained by considering all the associated costs (i.e., investment, losses, maintenance, reliability, and salvage value). Simulations were performed for various case studies representing the situations faced by utilities and based on the type of load transfer switches for a typical Finnish primary distribution substation. Moreover, a sensitivity analysis was also conducted based on DR penetration and LC penalty value. The investigation of results indicated that significant monetary saving can be gained by employing DR in substation transformers planning. These savings are higher for systems in which load transfer to NSS is conducted by remotely operated switches. The proposed optimization model is valid for all load types (such as residential, commercial, and industrial). For various load types, difference would be only in input parameter values and correspondingly output results would be different. The proposed model in this article was useful in optimal capacity planning of transformers with DR. The DR also offers others benefits to power systems players. Further research is required for optimum division of DR for its various benefits. Moreover, realization of these benefits (including one proposed in this paper) are interesting research directions. Acknowledgements The first author of this paper would like to acknowledge that this work is funded by the Aalto energy efficiency program through the SAGA project. References [1] M. Humayun, M.Z. Degefa, A. Safdarian, M. Lehtonen, Utilization improvement of transformers using demand response, IEEE Trans. Power Delivery 30 (Feb. (1)) (2015) 202–210. [2] M. Humayun, B.J.O. Sousa, M.Z. Degefa, S. Kazemi, M. Lehtonen, Markov model based assessment for redundancy mitigation in high voltage grids using demand response, Int. Rev. Electr. Eng. 8 (Jul.–Aug. (4)) (2013) 1349–1362. [3] M. Humayun, A. Safdarian, M.Z. Degefa, M. Lehtonen, Demand response for operational life extension and efficient capacity utilization of power transformers during contingencies, IEEE Trans. Power Syst. 30 (Jul. (4)) (2015) 2160–2169. [4] M. Humayun, M. Ali, A. Safdarian, M.Z. Degefa, M. Lehtonen, Optimal use of demand response for lifesaving and efficient capacity utilization of power transformers during contingencies, in: Proc. 2015 IEE PES General Meeting, Jul. 26–30, 2015, Denver, CO, USA, 2015. [5] H.L. Willis, Power Distribution Planning Reference Book, CRC Press, New York, 2010. [6] S. Heidari, M. Fotuhi-Firuzabad, S. Kazemi, Power distribution network expansion planning considering distribution automation, IEEE Trans. Power Syst. 30 (May (3)) (2015) 1261–1269. [7] O. Siirto, A. Safdarian, M. Lehtonen, M. Fotuhi-Firuzabad, Optimal distribution network automation considering earth fault events, IEEE Trans. Smart Grid 6 (Mar. (2)) (2015) 1010–1018. [8] EC Directive 2009/72/EC, EC Directive 2009/72/EC of the European Parliament and of the Council of 13 July 2009, concerning common rules for the internal market in electricity and repealing Directive 2003/54/EC, Off. J.Eur. Union L211 (Aug.) (2009).
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