5.3 Dynamic DNEP with energy storage systems
5.3.2 Solution evaluation
Constraint evaluation
For an MV-D network of n nodes (i.e., substations), the vector of peak active power demand at each node in year t is:
Pt= (P1t,sti, P2t,sti, . . . , Pnt,sti) (5.3) The accompanying vector of peak reactive power demand is:
Qt= (Qt,s1 ti, Qt,s2 ti, . . . , Qt,sn ti) (5.4)
5.3. Dynamic DNEP with energy storage systems
Let Pit,sti and Qt,si ti be the peak active power demand and the peak reactive power demand at node i in year t. If node i is not suitable for storage installation or there is no storage installed at node i in year t, then sti = 0; we have Pit,sti = Pit,0 and Qt,si ti= Qt,0i , which are the normal peak power demands when no peak-shaving technology is employed. If a BESS is installed at node i in year t, i.e., sti > 0, we have Pit,sti < Pit,0 and Qt,si ti < Qt,0i due to the peak-shaving effect. Because this thesis focuses on optimization methodologies for DNEP, we treat Ptand Qtas input data. By employing scenario-based load modeling techniques, DNEP practitioners can propose several plausible scenarios and estimate the corresponding load profile.
Interested readers can refer to the literature, e.g., network impacts under electric vehicle charging [3, 14], residential demand response [15], or distributed generation [6, 16].
To assess the feasibility of an expansion plan s = (x, y) for the dynamic DNEP problem, we need to evaluate the cable configuration x against the peak power demand Pt, Qt in each year t during the planning period, taking into account the peak-shaving effect of storage system y. Note that the cable configuration in each year t is determined by the decomposition heuristic. The solution codification in Equation 5.2 enables the capacity of each storage, in principle, to vary on an annual basis (i.e., from year to year). It is also possible to extend t into a stage of multiple years, where each stage covers a period of at most 5 years and at least 3 years.
The decomposition heuristic will then try to delay each cable installation by one stage of multiple years at a time. New cables and storage systems of a stage are assumed to be installed at the first year of that stage. Network feasibility in a stage, however, is evaluated against the peak power demand of the final year in that stage.
Because peak loads normally increase monotonically and the network configuration does not change during a stage, if the network capacity is sufficient at the final year of that stage, feasibility should also hold for previous years of the stage. Such a stage-by-stage planning approach is beneficial to the computing budget since the computationally expensive PFCs are only required at the final years of each stage rather than at every year. In this section, we employ the stage-by-stage planning approach.
Objective evaluation
Although we perform stage-by-stage planning, the investment cost CAPEX can still be calculated in a year-by-year formulation by the annuity payment scheme. The annuity for a BESS of type b ∈ S with a discount rate i = 4.5% is:
Annuity(b) = P rice(b) × i
1 − (1 + i)−tblif e (5.5) where tblif e= 10 years is the economic lifetime of all storage systems in this study.
P rice(b) is the acquisition cost (including construction cost) of a BESS of type b, which can be defined as:
P rice(b) = Capacity(b) × CkW h (5.6)
Theoretically, a BESS can be constructed up to any desired capacity by assembling multiple batteries. However, for the sake of simplicity, we constrain the capacity of each BESS to three options: type 1 (500 kWh), type 2 (1000 kWh), and type 3 (1500 kWh). These capacities are also reasonable regarding the normal capacities of MV/LV transformers. CkW h is similar to the marginal cost of increasing the capacity of the battery storage by 1 kWh.
Because we assume that the battery storage systems are movable, it is possible that a BESS is installed at a stage in the network, but it can be relocated to a different network in the next stage. The CAPEX of that BESS accounts for only the years in which the storage is present in the network. CAPEX for the BESS at a substation s ∈ S in a year t can be calculated as:
CAP EXstorage(s, t) =
Annuity(yst) if yst> 0
0 if yst= 0 (5.7) The CAPEX for new cable installations can be calculated as in Equation 4.3 of Chapter 4. The total CAPEX in a year t over the whole network is defined as:
CAP EX(t) = X
new cable c in [t0, thorizon]
CAP EXcable(c, t) +X
s∈S
CAP EXstorage(s, t) (5.8)
We minimize the net present value (NPV) of the total CAPEX over the planning period with a discount rate i:
CAP EXN P V =
thorizon
X
t=tX
CAP EX(t)
(1 + i)t−t0 (5.9)
Energy losses can be taken into account as operational expenditure OPEX, sim-ilar to Equation 4.7 in Chapter 4. Energy losses in year t consist of energy loss on electric cables and energy loss of storage systems.
Eloss(t) = Ecable loss(t) +X
s∈S
Estorage loss(s, t)
= Ppeak loss(t) × Tloss(t) +X
s∈S
Estorage loss(s, t) (5.10)
where Ppeak loss(t) is the peak loss which can be obtained from the PFC regarding the peak loads in year t. Note that the service time Tloss(t) here depends on the shape of the yearly load profile under the peak-shaving effects of the battery storage systems present in the network in year t. In this thesis, we also treat Tloss(t) and the annual energy losses of storage systems Estorage loss(s, t) as input data, which are device-specific and can be modeled by DNEP practitioners. As we conduct the dynamic planning on a stage-by-stage basis, we only need to perform PFCs for the final year of each stage and obtain the accurate value of peak loss on cables Ppeak loss(t) in that year. For the remaining years in the same stage, cable peak
5.3. Dynamic DNEP with energy storage systems
losses can be estimated by taking the assumption that the peak loss has a growth rate related to the load growth rate R as follows [17]:
Ppeak loss(t) = Ppeak loss(t − 1) × (1 + R)2 (5.11) We would like to find the expansion plan that minimizes the net present value (NPV) of the total cost CAPEX+OPEX over the planning period with a discount rate i:
COSTN P V =
thorizon
X
t=tX
CAP EX(t) + OP EX(t)
(1 + i)t−t0 (5.12)
5.3.3. Experiment setup
Benchmark network
We employ the MV-D Network 2 from Chapter 4 as the benchmark network. How-ever, for the purpose of DNEP with battery storage systems, we have some adap-tations as follows. All the cables in the current configuration are assumed to be a type-2 cable (i.e., 150mm2− 295A). Since the type-2 cable is relatively new, we also assume that cable replacements are not necessary, and only new cable connec-tion installaconnec-tions are allowed. The set of MV cable types from which new cable installations can be chosen is {2, 3} = {150mm2, 240mm2}.
The peak load scenario is estimated for the planning period 2015-2040, taking into account the increasing presence of electric vehicles, like in [3, 14]. The existing peak power demand is assumed to have an annual growth rate of R = 1%. Each year in the planning period is numbered from 0 (i.e., year 2015) to 25 (i.e., year 2040). Without any expansion activities, the current network capacity will become infeasible in the 3rd year, i.e., tX = 3. The remaining period is divided into five stages as: S1= [3 − 5], S2= [6 − 10], S3= [11 − 15], S4= [16 − 20], S5= [21 − 25].
The set of BESS types from which new storage installations can be chosen is S = {1, 2, 3} ≡ {500kW h, 1000kW h, 1500kW h}. Due to uncertainties about the actual price of storage systems in the future, we propose four scenarios of the marginal BESS cost CkW h= 1, 5, 10, and 20 EUR/kWh. Note that these (fictive) prices are much lower than the current actual construction costs of BESS (e.g., see [18]) since it is an on-going research technology. If we use the current BESS prices, which are quite expensive, the most economical expansion plan will only consist of traditional electric cable installations. Besides, our considered prices can be justified if subsidies are taken into account. The peak-shaving effect of BESS is modeled by employing a scenario-based peak load modeling technique [14, 16] while considering a BESS pilot project of DNO Enexis [19].
Optimization algorithm
We employ GOMEA-BX-M to solve DNEP with BESS for the benchmark network because GOMEA-BX-M has been shown to be the best solver in previous exper-iments in this thesis. We consider two cases for optimization: 1) minimizing the investment cost CAPEX (i.e., Equation 5.9), and 2) minimizing the total cost that combines both the investment cost CAPEX and the capitalized energy losses OPEX
(i.e., Equation 5.12). In each case, we set up one scenario where no BESS is used (i.e., the traditional DNEP) and four scenarios with different BESS prices: 1, 5, 10, and 20 EUR/kWh. For every scenario, we run GOMEA-BX-M 10 times indepen-dently with the computing budget of 500000 solution evaluations in each run. The adapted Harik-Lobo scheme (see Chapter 4) is employed so that we do not need to set the population size for the solver. The best expansion plans obtained in each scenario are presented in the following sections.