Dynamic reconfiguration of active distribution network considering multiple active management strategies

To make full use of various active management resources in ADN to improve the economic efficiency, a dynamic reconfiguration model of active distribution network considering multiple active management (AM) strategies is proposed in this paper. The AM strategies including the configuration of energy storage system, output power controlling of distributed generation, reactive power compensation with static var compensators and packet capacitor switching, tap adjusting with on-load tap changer, and demand side response management. The model tries to minimize the total costs with respect to various operating constraints. Several linearization techniques are applied to formulate the dynamic reconfiguration problem into a mixed-integer linear programming (MILP) model, which guarantees global optimal solution and also reduces the computational difficulty significantly. Finally, the validity and effectiveness of the proposed dynamic reconfiguration model is verified on the IEEE 33-node distribution network system.

IOP Publishing doi: 10.1088/1755-1315/227/3/032036 2 the topology of the distribution network by altering the state of the remote control switch, thereby achieving flexible network structure optimization [7]. In [8], a new method for dynamic reconfiguration to maximize loadability of radial distribution systems is presented, and it is solved by a fuzzy adaptation of the evolutionary programming algorithm. In [9], a day-ahead and real-time optimal dispatch model considering energy storage and controllable distributed generation of ADN is built, and an improved particle swarm optimization algorithm is adopted to solve the models. In [10], a day ahead scheduling model considering the flexible load, the energy storage, reactive power compensation devices is built. And multi-objective particle swarm optimization algorithm is used to solve this problem.
However, the existing papers about dynamic reconfiguration rarely consider AM strategies or just consider part of them, which don't make the most of their economic value to optimize the economy operation of ADN. Meanwhile, the papers mentioned above use different kind of intelligent algorithm to solve MINLP problem, which could only get locally optimal solution and the convergence speed is slow and they depend on specific system parameters.
The contributions of this paper are as follows. 1) A dynamic reconfiguration of ADN considering multiple AM strategies is proposed. The model consider comprehensive AM strategies ( the configuration of ESS, output power controlling of DG, reactive power compensation with SVC and packet SC, tap adjusting with OLTC, and DRM), which could reduce the operation cost more efficiently.
2) Various linearization methods are applied to transform the MINLP model are difficult to solve into a MILP model, which could be solved with high computing efficiency. And different from the intelligent algorithm, MILP can get globally optimal solution with less iterations and is adapt to wildly varying circumstances.

Dynamic reconfiguration of ADN
In this section, the formulation of the dynamic reconfiguration of ADN is presented. The model considered multiple active management strategies with various operation constraints. The optimization model is set up as follows:

Objective function
The objective function of this model is to minimize total operation cost: (1) The meaning and calculation method of each part of the objective function in equation (1) are as follows: 1) Power purchase cost where N T is the set of look-ahead time periods (e.g., 24 h); P C is the electricity price; and GRID t P is the active power purchased from substation during time t.
2) DG operation cost where N DG is the set of DG; DG C is the operation and maintenance cost of DG; and , DG i t P is the output power of the ith DG during time t.
3) DRM cost DRM measures in this paper refer to common interruptible load (IL) measures. ILs are attracted to sign a contract with DSO to interrupt or reduce their demand during peak load or emergency with certain economic compensation. In (4) where N ESS is the set of ESS; ESS C is the cost of ESS; , C i t P and , D i t P are the charging power and discharging power of the ith ESS during time period t, respectively.

Constraints
, , , The status of the switch is defined by the binary variable , ij t z , which takes 1 if the switch is closed in period t and takes 0 otherwise. And i N is the set of all buses. 3) Branch capacity constraint where ij S is the apparent power capacity of branch ij.

4) Voltage magnitude constraint
Equation (13) where , k t T is the location of transformer tap during period t. 7) Output power controlling of DG ,min ,max , , ,1 , , ,min ,max , where ,max ESS i P is the maximum charging/discharging power of the ith ESS; , where ,max DRM i P is the upper limit for IL.

Linearization techniques used in the method
Take the linearization method in [11], constraints (8) and (9) can be approximated by the following linear expressions: Furthermore, the quadratic term 2 Constraint (11) is a circular constraint, which can be approximated by an inscribed regular polygon [11] as shown in Figure 1.   (6) and (7) can be approximated by the following linear expressions: 1 , , ki t ij t ki t ki t ij t ki t P -z P z P -z P     (33) The rest three terms can be reformulated similarly.

Case study
The proposed model is tested on modified IEEE 33-bus radial distribution system [4] which consists of 5 tie switches and 32 sectionalize switches. The network diagram proposed is shown in Figure 2. Furthermore, a WT is installed in node 24, a SVC device is installed in node3, a SC device is installed in node 30, and an ESS device is installed in node 21. And the load curve is presented in Figure 3. All tests are solved by using CPLEX of GAMS on a personal computer with an Intel Core: i5-6400 2.70 GHz CPU and 8 GB of RAM.
The remote-controlled switches are s11, s13, s14, s16, s27, s28, s33, s34, s35, s36, s37, s38. The optimal configuration of the feeder can be obtained using the proposed approach, as summarized in Table 1, where the opened switches are listed for each time interval and the remainder of the switches is closed. The minimum total cost is ¥53837, of which the DRM cost is ¥1224 and the ESS cost is ¥1337. The calculation time is 02′33″.   s11, s16, s27, s33, s35 23-24 s11, s13, s16, s27, s33 Without considering AM strategies, the total cost of dynamic DNR is ¥54003. Compared with ¥53837 of dynamic DNR with AM strategies, the total cost decreases 0.3%,i.e., AM strategies can save ¥166 for one day, corresponding to ¥60590 for a year, which is a significant cost saving.

Conclusions
This paper proposed a dynamic reconfiguration model with the objective function of minimizing total operation costs. The model applies multiple AM strategies to optimal the economy of system operation, which could better reflect the development requirements of ADN and accord with the trend of future smart distribution network. The 33-bus case verified that AM strategies can significantly increase economic benefits to ADN by comparing with dynamic DNR without AM strategies. During the model solving process, multiple linearization methods are adopted to convert the MINLP model into a MILP problem, which can be easily solved by commercial solver and can guarantee both effectiveness and validity of the solution.

Acknowledgement
This paper is supported by National Natural Science Foundation of China (51407106).