Economy and Management of energy systems

Economy and Management of energy systems

Basic revision,Specific

costs

2

400 kV220 kV

110 kV 22 kV 35 kV

0.4 kV

j = 0 1 2 3 4 5 6 7

Power plant

gn/vvn vvn/vvn vvn/vn vn/nn Consumption

ČEZ, a.s.

Elektrárny Opatovice, a.s.

Energotrans, a.s.

Sokolovská uhelná, a.s.

…..

Transmission grid:

ČEPS, a.s.

Distribution grids – PRE, ,ČEZ , E.ON

Transmission Voltage levels:

400 kV (2900 km); 220 kV (1440 km); 110 kV (105 km)

Distribution Voltage levels:

110 kV � 22 (35) kV � 0,4 kV ; 35 kV

Generator Voltage � (Extra) High Voltage � (Extra) Low Voltage

Electricity Grid Structure

4 000

4 500

5 000

5 500

6 000

6 500

7 000

7 500

0 4 8 12 16 20 24

t (hod)

P (M

W)

Basic

Semi-peal

Peak

Sources within energy systems: Basic – Nuclear PP, Hydro PP (flow!), Modern condensing power plants, Heating plants with back pressureturbines, purchase from UCTE

Semi-peak – condensing power plants,Hydro PP (accumulative)

Peak – Pumping Hydro PP, Gas PP

RES - basic, semi-peak and peak sources (small hydro, wind, PV, biomass,geothermal…)

Load diagram and energy sources

4

District heating systems

Primary source

Předávací stanice

Dálkový napáječ – Primary grid

Secondary grid

Tertiary grid

Customers

Customers

Local Peak

Source

Heat delivery: - Steam piping - Hot water piping (Heat lines > 110 OC; Primary and secondary grids) - Hot water piping (Heat lines < 110 OC; Tertiary grids)

Basic revision Time of the Maximum Load (Doba využití maximálního zatížení)

m

T

m

T

m PW

P

dttPT ��

�0

)(

Time of the Full Losses (Doba plných ztrát)

20

2

20

2

20

2 )(

cos33

cos3)(3

3

)(3

m

T

m

T

m

T

zm

zTz P

tP

UPR

dtUtPR

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TT

TTT mm

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In state regulation:

T … Time of the observed period

Energy characteristics of transformer

Energy characteristics of transformer represents the dependency of energy losses on the load. No-load Losses (Hysteresis losses, Magnetostriction,…) (in iron) – Po,; these losses are permanent and do not depend on the load!

Load Losses (Winding resistance) (in copper) – Pkn, Jouls losses; these losseare fluctuating a DO depend on the load.

S … load Sn … nominal output of transformer

2

2

nknoz SSPPP ��

Energy losses of transformer

zn

mknprozr TSSPTPW 2

2

���

• Wzr … annual energy losses in transformer

• Tpr … annual working time of transformer • Sm … annual maximum load of transformer

Power factor compensation

Power factor compensation benefits: Ič - active current 1) Smaller cross-section of the power lines I - apparent current 2) Lower investment cost of the new power lines Ij - blind current 3) Lower drop of potential 4) Decrease of losses within the power lines 5) Better transients in the power grid

Inductive consumption

Compensator

Power grid with power factor compensation

Ič

Ij

I

I´j

I´

Ik

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�k

2)sincos(3

)sincos(3

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IjIRPIXRIU

ztr

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Specific costs for electricity generation and transportation

Fixed costs (FC) �are independent on the volume of the production

(power generation) �are including costs such as: depreciations,

interests, salaries, material, indirect costs, maintenance and repair….

Variable costs (VC) �are dependent on the production (power

generation) � for our case are usually reduced to fuel costs

Structure of costs (expenditures) of „energy investments“ in time

One time costs (directly connected with construction)

� Preparation of construction, project (blueprints,…), construction, installation of equipment, measurement and regulation.

� Purchase of stockpile fuel, spare parts, initial training of employees

Annual Fixed Costs (during operation)

� Fixed Capital Costs (NS): - loan interests - depreciations

- leasing repayment

Specific costs for electricity generation and transportation

� Fixed operating costs (NPS) Costs of operation: - Salaries of employees - Operating material - Maintenance and repair - Insurance, taxes, fees, …Costs of management: - Salaries, education, audits, … � Variable operating costs (NPP) – costs that are dependent on the

production - Fuel (transportation included) - Purchase of electricity, heat and other forms of energy - Costs of waste disposal

- Emission fees

Production costs

• Production costs (NVYR) Operating Costs (NP = NPP + NPS) + Depreciations (NO) = Actual Costs (NVL) + Interests (NÚ) = Production costs (NVYR)

13

iaiopopúvlvyr NpNpNNNNNNNú

����������

Depreciations Interests

ANaNNppNNN pTžipaoipvyr �������� )(

iTž NaA �� Annuity - average annual value derived from the investment costs. Present value of the annuity (taken for the economic lifetime) gives the value that equals the investment costs

aoTž

Tž

Tž ppr

rra ������

�1)1(

)1(Proportional annuity:

Tž … economic lifetimer … discount rate po … proportional depreciations (po = 1/Tž) pa … proportional annuity interest

14

Specific costs for power generation

)( pmsmpsmpsvyr nTnPnWnPNNN ����������

Pm … annual maximum output (MW) W … annual energy production (MWh) Tm … time of the Maximum Load (hod)

ns … specific fixed costs based on output (Kč/MW) np … specific variable costs based on energy (Kč/MWh)

The higher Tm – the lesser is the influence of fixed costs within the production costs „Každá cena stanovená jen na základě průměrných výrobních nákladech (jednosložková cena … Kč/MWh) nic nevypovídá o “vnitřku“, o stavu, který odběratel vytváří.“

pm

s

mm

vyrvyrvyr n

Tn

TPN

WN

n ���

�� (Kč/MWh) … average (specific) production costs of 1 unit of production

15

Costs division methods – CHP (Combined Heat and Power)

� Used in the situations when it is impossible to reliably distinguish costs for boiler and steam engine.

� The aim is to correctly set the costs for electricity production and heat production (to calculate the proper electricity and heat prices)

Methods: - physical - value index

A) Physical Methods

1. Calorific Method � The overall costs are divided in a ratio of heat energy in steam for electricity

production and heat energy in steam that directly delivered to end customers. � The economic effect from CHP goes to electricity production

koa

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koa

odbakale

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koa

koptkalt

koa

ptakale

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� ia … enthalpy of admission iodb … enthalpy of take-off ipt … enthalpy of back pressureiko … enthalpy of condensate

16

2. Thermodynamic Method � Heat energy in steam for electricity production from CHP is set to the value that is

corresponding with heat energy of alternative condensing power plant . � The economic effect from CHP goes to heat production.

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ka

odbatde

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ka

kpttdt

ka

ptatde

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� ik … emission enthalpy ( before condenser)

3. Exergy Method � The overall costs are divided in a ratio of exergy in steam used for electricity production

and heat production � Exergy - the value of energy (within the overall energy) that can be transform into useful

mechanical labor

17

B) Value index Methods

1. Triangle Method � The overall costs of heating power plant (also the economic effects from CHP) are

divided based on the choice of alternative heating plant (only heat without electricity production) and alternative condensing power plant

nt

ne

QnEnN tevyr ����

ne … specific costs of electricity production (Kč/MWh) nt … specific costs of heat production (Kč/GJ)

2. Differential Method � The one form of energy is priced with fixed specific costs (electricity) and costs for the

other form of energy (heat) is the complement (to the total costs)

3. Business Method � Reflects the situation when the price of electricity produced in heating plant (CHP) is

given. � The costs for heat is the difference between the total costs and the incomes for the

electricity.

Why marginal costs?� The main aim of LRMC (Long Run Marginal Costs) calculation is to represent the

production costs of the change of electricity consumption or rather of electricity production from the macroeconomic point of view.

� It can be used for the purposes of economic effectiveness calculation, development of new tariffs, feed-in tariffs, etc.

Marginal costs

•TC=FC+VC •ATC=TC/Q •AFC=TFC/Q •AVC=TVC/Q•ATC=AFC+AVC •TP=TR – TC •AP=TP/Q • MC curve intersect with AC curve in minimum of AC• If MR=MC, revenue is maximized

TC – total costs VC – variable costs FC – fixed costs AC – average costs TR – total revenueAR – average revenue MC – marginal costs MR – marginal incomes TP – total profit

Marginal costs

Marginal costs definition The marginal cost of an additional unit of output is the cost of the additional inputs needed to produce that output. More formally, the marginal cost is the derivative of total production costs with respect to the level of output.

12

12

QQTCTC

dQdTCMC

��

��

SRMC (Short Run MC) : FC = const �

LRMC (Long Run MC) : FC ≠ konst �

dQdVCMC �

dQdTCMC �

Tangent definition Secant definition

SRMC … Short Run Marginal Cost) Defined as incremental production costs caused by the increase of supply in case of unchanged capacity of production or transportation facilities.SRMC are often extended with losses caused by non-supply of electricity

LRMC … Long Run Marginal Cost � Defined as incremental production costs caused by the increase of supply � Include the investments into required production and transportation capacity

If the electricity supply system is developed in optimal way than:

Tžipstprndpr aNNNNN ����������LRMCSRMC �

�Npr … increase of variable operating costs (costs for losses)

�Nnd … increase of costs caused by non-supply

�Npst … increase of fixed operating costs (maintenance, repair)

�Ni�aTž … increase of annuity value of investment costs

Costs caused by non-supply (supplier x consumer): • direct – revenue losses, profit margin losses… • indirect – back-up sources, switching to different transmission lines • system – repair costs of facilities that are unscheduled built

1) System Method

nv

zvopt zv 0,9 0,99 0,999 0,9999

Fixed part of production costs within electricity supply system

National economic costs caused by non-supply

National economic costs caused by securing the supply

zvopt … Optimum of supply safeguard

Marginal costs – calculation methods

� System method (of MC calculation) is based on experiments on mathematical – economical model of electricity supply system

� System method includes variable and fixed operating costs and annuity value of investments of all sources within electricity supply system

2) Method of representatives � Assume the balance between demand and supply within electricity supply system. Any

additional production (without the increase of installed capacity) is impossible. Therefore:

gridsandsourcesnewACLRMC ___�� This method is calculating only with chosen types of sources – „closing power plants“

(development and operation is not limited in the near future) � Closing power plant is such power plant that is „closing“ the balance of electricity

supply system

Vylučující podmínky závěrných elektráren: - nedostatek paliva- nedostatek lokalit pro výstavbu - ekologické problémy - závislost výroby elektřiny na jiné hlavní výrobě (teplárny), na klimatických podmínkách

Obecný vztah:

� � wEzwmpsSTžSiSpsETžEiErvsmzpm nkTpanpankkkkn ������������� )()(

niE … měrné investiční náklady nových závěrných elektráren (kč/kW)

niS … měrné investiční náklady nových sítí (kč/kW)

km … koeficient účasti maxima odběratele na maximu soustavy (-)

kvs … koeficient vlastní spotřeby (-)

kzp, kzw … koeficient ztrát výkonu, resp. práce v sítích soustavy (-)

kr … koeficient zálohy výkonu v závěrných elektrárnách (-)

ppsE … roční poměrné stálé provozní náklady elektráren

ppsS … roční poměrné stálé provozní náklady sítí

Tm … roční doba využití Pm odběratele

nwE … měrné proměnné náklady výroby elektřiny (Kč/kWh)

aTžE, aTžS … poměrná anuita za ekonomickou dobu životnosti závěrných elektráren a sítí