Long-Term Smart Grid Planning Under Uncertainty Considering Reliability Indexes

Abstract

The electricity sector is fast moving towards a new era of clean generation devices dispersed along the network. On one hand, this will largely contribute to achieve the multi-national environment goals agreed via political means. On the other hand, network operators face new complexities and challenges regarding network planning due to the large uncertainties associated with renewable generation and electric vehicles integration. In addition, due to new technologies such as combined heat and power (CHP), the district heat demand is considered in the long-term planning problem. The 13-bus medium voltage network is evaluated considering the possibility of CHP units but also without. Results demonstrate that CHP, together with heat-only boiler units, can supply the district heat demand and contribute to network reliability. They can also reduce the expected energy not supplied and the power losses cost, avoiding the need to invest in new power lines for the considered lifetime project.

Nomenclature

13.1.1 Indices

c :

Line options

e :

Energy storage systems (ESSs)

g :

Distributed generator (DG) unit

h :

Heat-only boiler unit

hl:

Heat load

hp:

CHP heat power

i :

Electrical buses

j :

Electrical buses

l :

Loads

s :

Scenarios

sp:

External suppliers

v :

Electric vehicles parking lot (EV)

w :

Transfer buses

13.1.2 Parameters

λ :

Failure rate

ρ :

Line resistivity at operating temperature (Ω × mm²/km)

BNF:

Benefit from the solution applied (€)

CostEENS:

Expected energy not supplied cost (€)

CostGCP:

Generation curtailment power cost (€)

CostINV:

Initial investment in new lines (€)

CostM:

Maintenance cost (€)

CostPL:

Power losses cost (€)

dr:

Discount rate

EENS:

Expected energy not supplied

EVPI:

Expected value of perfect information

FOR:

Forced outage rate

FOR_(i,j,c) :

Forced outage rate between bus i and bus j according to the chosen line option c

h :

Number of service hours for the electric conduits per year

I :

Current that flow in the line (A)

Investment:

Total investment for the planning project (€)

J _eco :

Economic current density (A/mm²)

k′ and k ^″ :

Constants that depend on the type of service (one or three phases)

L :

Line length (km)

n :

Number of active conductors

NB:

Number of buses

nDG:

Number of DG units

NL:

Number of distribution network lines

NO:

Number of line options

NPV:

Net present value

NS:

Number of scenarios

NW:

Number of transfer buses

p :

Energy price (€/kWh)

P _{ChargeLimit(e)} :

Maximum charge rate of energy storage systems (kW)

P _{DGMaxLimit(g)} :

Maximum active power of DG (kW)

P _{DGMinLimit(g)} :

Minimum active power of DG (kW)

P _{DGScenario(g,s)} :

Forecasted generation of DG (kW)

P _{DischargeLimit(e)} :

Maximum discharge rate of energy storage systems (kW)

P ^máx _(i,j,c) :

Maximum admissible line flow between bus i and bus j according to the chosen line option c

P _SMaxLimit :

Maximum active power of suppliers (kW)

P _SMinLimit :

Minimum active power of suppliers (kW)

P _Supplier(sp) :

Active power of external suppliers

q :

Constant value dependent of the line/cable type

r :

Repair time (h)

R :

Line resistance (Ω/km)

S :

Load (kVA)

SAIDI^max :

Maximum Limit to System Average Interruption Duration Index Limit (h/consumer × year)

SAIFI^max :

Maximum Limit to System Average Interruption Frequency Index (interruption/consumer × year)

S _cc :

Line section (mm²)

sf _v :

Simultaneity factor

t :

Project lifetime (years)

T :

Number of total hours of a year

T _e :

Time equivalent (h)

U :

Unavailability

13.1.3 Variables

a _ESS(e,s) :

Discharging status of the energy storage systems

D _(g) :

Fictitious load of each distributed generator g

d _(i,j,c) :

Fictitious flow associated with branch i,j for c line option

hb_(h,s) :

Heat power for boiler unit h in scenario s

hchp_(hp,s) :

Heat power for CHP unit hp in scenario s

hload_(hl,s) :

Heat demand for hl heat load in scenario s

P _(i,j,c) :

Power flow between bus i and bus j according to the chosen line option c

PC¹ :

Expected planning cost for the first stage

PC² :

Expected planning cost for the second stage

P _Charge(e,s) :

Active power charging of energy storage systems (kW)

P _{Discharge(e,s)} :

Active power discharge of energy storage systems (kW)

P _Charge(v,s) :

Active power charging of EV parking lot (kW)

P _GCP(g,s) :

Generation curtailment power of non-dispatchable DG units (kW)

P _Load(l,s) :

Active power load for l load scenario s

SAIDI:

System Average Interruption Duration Index (h/consumer × year)

SAIFI:

System Average Interruption Frequency Index (interruption/consumer × year)

VSS:

Value of stochastic solution

x _ESS(e,s) :

Charging status of the energy storage systems

z _(w) :

Binary variable related to the transfer buses

13.1.4 Sets

Ω _B :

Set of buses

Ω _BS :

Set of substation buses

Ω _BT :

Set of transfer buses

Ω _DG :

Set of DG

Ω ^d _DG :

Set of dispatchable DG

Ω ^nd _DG :

Set of non-dispatchable DG

Ω _E :

Set of ESS

Ω ^b _E :

Set of ESS bus

Ω _heatboiler :

Set of heat boiler

Ω _heatload :

Set of heat load

Ω _hp :

Set of CHP heat power

Ω _L :

Set of loads

Ω ^b _L :

Set of load buses

Ω _l :

Set of lines

Ω _SP :

Set of external suppliers

Ω ^b _SP :

Set of external supplier buses

Ω _V :

Set of EV

Ω ^b _V :

Set of EV buses