XYLENE POWER LTD.

TRANSMISSION/DISTRIBUTION COST APPORTIONING

By C. Rhodes

INTRODUCTION:
This web page addresses transmission and distribution costs that must be re-apportioned to effectively implement private sector distributed electricity generation within the Province of Ontario.

ELECTRICITY GRID:
The electricity grid in Ontario is actually a collection of interconnected distribution systems that are owned and maintained by separate parties. Most of the major generators are connected to the high voltage transmission system that is maintained by Hydro One. This high voltage transmission system is in turn connected to many lower voltage distribution systems that are maintained by Local Distribution Companies (LDCs). Rural Local Distribution Systems are also often operated and maintained by Hydro One. Most end users obtain their electricity from LDCs.

At every point where electricity enters or leaves the high voltage transmission system there is a directional kwh meter. Similarly at every point where electricity enters or leaves a local distribution system there is a directional kWh meter. There are some unmetered loads such as street lighting, but generally the LDCs have accurate records as to the number, size and performance characteristics of these loads. For the purposes of calculations presented herein these loads can be considered as metered.

The high voltage transmission system can be considered to be a distribution system with generators and LDCs as customers that exchange energy.

Each LDC has a distribution system with the transmission system that is maintained by Hydro One as one customer and with distributed generators and end consumers of electricity as the other customers. The LDC's customers exchange energy amongst themselves.

DEFINITION OF TERMS:
Cht = total cost that Hydro One must apportion amongst its customers;
Chi = costs directly related to the high voltage transmission system;
Cjt = total costs that LDCj must apportion amongst its customers;
Cji = costs directly related to LDCj;
Ckt = total costs that LDCk must apportion amongst its customers;
Cki = costs directly related to LDCk
 
Pg = central generator output power fed to Hydro One transmission;
Pj = power flowing from Hydro One transmission to LDCj;
Pk = power flowing from Hydro One transmission to LDCk;
Pjt = total power indicated on all LDCj electricity meters;
Pkt = total power indicated on all LDCk electricity meters.

COST APPORTIONED TO CENTRAL GENERATORS:
Assume that there is no electricity generation within the LDCs. This is the special case that approximately pertains at this time in Ontario due to a rate structure that acts as a disincentive for LDC connected distributed generation.
If transmission loss is neglected, conservation of energy requires that:
Pg = Pj + Pk + ...
If distribution loss in LDCj is neglected, conservation of energy requires that:
Pj = Pjt/2
If distribution loss in LDCk is neglected, conservation of energy requires that:
Pk = Pkt/2

Assume that costs are apportioned amongst customers in proportion to absolute measured power. This is a simplification for demonstration purposes.

The cost billed to Hydro One transmission by LDCj for use of the LDCj distribution system is:
(Pj / Pjt) Cjt.
The total cost billed to Hydro One transmission by LDCb for use of the LDCb distribution system is: (Pk / Pkt) Ckt.
Thus the total cost Cht that Hydro One transmission must apportion amongst its customers is given by:
Cht = Chi + (Pj / Pjt) Cjt + (Pk / Pkt) Ckt + ...
= Chi + (1/2) (Cjt + Ckt + ...)

The total cost Cjt that LDCj must apportion amongst all its customers is given by: Cjt = Cji +(Pj /(Pg + Pj + Pk + ...)) Cht
The total cost Ckt that LDCk must apportion amongst all its customers is given by: Ckt = Cki +(Pk /(Pg + Pj + Pk + ...)) Cht
Thus:
Cjt + Ckt + ...
= Cji + Cki + ... + ((Pj + Pk + ...)/(Pg + Pj + Pk +...) Cht
= Cji + Cki + ... + Cht/2

Substituting this equation into the previous equation for Cht gives:
Cht = Chi + (1/2) (Cjt + Ckt + ...)
= Chi + (1/2) (Cji + Cki + ... + Cht/2)

Rearranging this equation gives:
(3/4) Cht = Chi + (1/2) (Cji + Cki + ...)

Multiply both sides of this equation by (2/3) to get:
Cht / 2 = (2/3) Chi + (1/3) (Cji + Cki + ...)

Hence the cost billed by Hydro One transmission to the central generators is:
(Pg /(Pg + Pj + Pk + ...) Cht = Cht / 2
= (2/3) Chi + (1/3) (Cji + Cki + ...)

SUMMARY:
This important result states that, subject to the assumptions that there is negligible generation within the LDCs and that transmission and distribution losses are negligible, the central generators must bear 2/3 of the high voltage transmission system costs and 1/3 of the lower voltage system distribution costs. Hence, end users and distributed generators that are directly connected to LDCs must bear 1/3 of the high voltage transmission system costs and 2/3 of the lower voltage system distribution costs, so that the transmission and distribution systems achieve 100% cost recovery.

HYDRO ONE NON-ENERGY RATE:
For normal density Hydro One customers the average transmission and distribution loss is 9.2%. For customers with monthly peak demands less than 50 kW the existing grid connection charges are currently broken down by distribution, debt retirement, transmission and regulation. On the basis of Ontario Energy Board (OEB) approved Hydro One 2006 rate for normal density residential customers the incremental cost per kWh is typically:
($.0218(distribution) + $.0070(debt retirement)) + 1.092(distribution loss) X ($.0094(transmission) + $.0062(regulation))
= $.0288 + 1.092($.0156)
= $.0458 /kWh plus GST.
If there was no distribution loss this number would be:
$(.0218 + .0070 + .0094 + .0062) / kWh = $.0444 / kWh

TORONTO HYDRO NON-ENERGY RATE:
The corresponding 2006 Toronto Hydro rate is:
($.0103(transmission) + $.0184(distribution) + $.0015(market transition) + $.0062(regulation) + $.0070(debt reduction)) / kWh = $.0434 / kWh

Note that the two rate structures have total non-energy charges that agree to within $.001 / kwh

REALLOCATED TRANSMISSION/DISTRIBUTION COSTS:
For General Service customers in Toronto with monthly demands less than 50 kW Toronto Hydro in 2006 indicated that the transmission charge was $.0103 / kWh and the distribution charge was $.0184 / kWh. Hence the amount of these charges that should be borne by the central generators is given by:
(2/3)($.0103 / kWh) + (1/3)($.0184) = $.013 / kWh
and the amount that should be borne by distributed generators and end users is given by:
(1/3)($.0103 / kWh) + (2/3)($.0184) = $.0157 / kWh

The reallocated transmission/distribution costs will increase the Hourly Ontario Electricity Price (HOEP) by about $.013 / kwh and should decrease load customer transmission/distribution costs by about $.013 / kWh. This reallocation has the effect of increasing the value of electricity from distributed generation that is exported to the grid by:
2 X $.013 / kWh = $.026 / kWh

This web page last updated March 2, 2009.