In such cases the limitation of downward reserve and correspond ingly over

# In such cases the limitation of downward reserve and

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reserve is required to be provided by conventional units . In such cases, the limitation of downward reserve and correspond- ingly over-generation problem will be more pronounced with higher renewable penetration . CHEN et al. : POWER SYSTEM CAPACITY EXPANSION UNDER HIGHER PENETRATION OF RENEWABLES CONSIDERING FLEXIBILITY 6243 In light of the system reliability requirement, the total in- stalled capacity should be no less than the required capacity limit: M k i =1 ¯ I i k + λ w k · ¯ I w k + λ s k · ¯ I s k D max k (10) where λ w k and λ s k are the capacity credits for wind and so- lar power in region k , respectively; D max k represents the total capacity requirement to maintain reliability standards. For sim- plicity in the modeling, we use fixed capacity credits for wind and solar respectively, although the value of capacity credit for wind and solar is non-linear with respect to the total capacity. D. Modeling for the Operation and Investment for Storage A novel linear simulation model for energy storage is pre- sented in this section to represent the costs and constraints asso- ciated with their investment and operation, considering multiple geographical areas and different storage types. The overall costs for storage systems include both amortized investment and operational costs formulated as: C es = N a k =1 N e s z =1 a p,z k · ¯ I p,z k + a e,z k · ¯ I e,z k + c es,z k · T t =1 p dis,z t,k + p ch,z t,k · Δ t (11) where a p,z k and a e,z k are the power-specific and energy-specific amortized investment costs for the z th category of energy stor- age in region k . The power-specific cost is related for example to the rotating synchronous machines in a pumped hydro unit, or to the power electronic rectifier/inverters in a battery stor- age system, or to the costs for anodes and cathodes in the case of flow battery . The energy-specific cost is related to the reservoir for a pumped hydro system  or to the cost for the solution included in a flow battery. c es,z k is the operational cost for the z th category of energy storages in region k . The opera- tional cost is proportional to both the charging and discharging power. ¯ I p,z k and ¯ I e,z k define the corresponding maximum power and energy capacities for the newly installed storage systems. They satisfy: ¯ I p,z k 0 , ¯ I e,z k 0 (12) 0 p dis,z t,k ¯ I p,z k (13) 0 p ch,z t,k ¯ I p,z k (14) The energy balances of electric storage systems are repre- sented by: e es,z t +1 ,k = e es,z t,k + γ ch,z es · p ch,z t,k · Δ t 1 γ dis,z es · p dis,z t,k · Δ t γ self,z es · e es,z t,k (15) where γ ch,z es , γ dis,z es and γ self,z es indicate respectively the charg- ing/discharging efficiency and energy loss (self-discharge) rate for the z th category of energy storages; e es,z t,k represents the en- ergy level at time t for the z th category of energy storage in region k , constrained by the installed capacity: ν z es · ¯ I e,z k e es,z t,k ¯ ν z es · ¯ I e,z k (16) where ν z es and ¯ ν z es represent the minimum and maximum levels of residual energy in the storage system respectively. For certain types of storage systems, deep-discharge will significantly re-  #### You've reached the end of your free preview.

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